subject:(Perverse sheaves)

Louisiana State University

1. Rider, Laura Joy. Mixed categories, formality for the nilpotent cone, and a derived Springer correspondence.

Degree: PhD, Applied Mathematics, 2013, Louisiana State University

URL: etd-06212013-132011 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2732

► Recall that the Springer correspondence relates representations of the Weyl group to perverse sheaves on the nilpotent cone. We explain how to extend this to… (more)

Subjects/Keywords: formality; perverse sheaves; nilpotent cone

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APA (6^th Edition):

Rider, L. J. (2013). Mixed categories, formality for the nilpotent cone, and a derived Springer correspondence. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-06212013-132011 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2732

Chicago Manual of Style (16^th Edition):

Rider, Laura Joy. “Mixed categories, formality for the nilpotent cone, and a derived Springer correspondence.” 2013. Doctoral Dissertation, Louisiana State University. Accessed April 13, 2021. etd-06212013-132011 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2732.

MLA Handbook (7^th Edition):

Rider, Laura Joy. “Mixed categories, formality for the nilpotent cone, and a derived Springer correspondence.” 2013. Web. 13 Apr 2021.

Vancouver:

Rider LJ. Mixed categories, formality for the nilpotent cone, and a derived Springer correspondence. [Internet] [Doctoral dissertation]. Louisiana State University; 2013. [cited 2021 Apr 13]. Available from: etd-06212013-132011 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2732.

Council of Science Editors:

Rider LJ. Mixed categories, formality for the nilpotent cone, and a derived Springer correspondence. [Doctoral Dissertation]. Louisiana State University; 2013. Available from: etd-06212013-132011 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2732

Louisiana State University

2. Russell, Amber. Graham's variety and perverse sheaves on the nilpotent cone.

Degree: PhD, Applied Mathematics, 2012, Louisiana State University

URL: etd-06232012-104447 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3631

► In recent work, Graham has defined a variety which maps to the nilpotent cone, and which shares many properties with the Springer resolution. However, Graham's… (more)

Subjects/Keywords: graham's variety; nilpotent cone; perverse sheaves

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APA (6^th Edition):

Russell, A. (2012). Graham's variety and perverse sheaves on the nilpotent cone. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-06232012-104447 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3631

Chicago Manual of Style (16^th Edition):

Russell, Amber. “Graham's variety and perverse sheaves on the nilpotent cone.” 2012. Doctoral Dissertation, Louisiana State University. Accessed April 13, 2021. etd-06232012-104447 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3631.

MLA Handbook (7^th Edition):

Russell, Amber. “Graham's variety and perverse sheaves on the nilpotent cone.” 2012. Web. 13 Apr 2021.

Vancouver:

Russell A. Graham's variety and perverse sheaves on the nilpotent cone. [Internet] [Doctoral dissertation]. Louisiana State University; 2012. [cited 2021 Apr 13]. Available from: etd-06232012-104447 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3631.

Council of Science Editors:

Russell A. Graham's variety and perverse sheaves on the nilpotent cone. [Doctoral Dissertation]. Louisiana State University; 2012. Available from: etd-06232012-104447 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3631

Louisiana State University

3. Minn-Thu-Aye, Myron. Multiplicity formulas for perverse coherent sheaves on the nilpotent cone.

Degree: PhD, Applied Mathematics, 2013, Louisiana State University

URL: etd-07082013-113917 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3732

► Arinkin and Bezrukavnikov have given the construction of the category of equivariant perverse coherent sheaves on the nilpotent cone of a complex reductive algebraic group.… (more)

Subjects/Keywords: perverse coherent sheaves; derived categories of coherent sheaves; representation theory

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Minn-Thu-Aye, M. (2013). Multiplicity formulas for perverse coherent sheaves on the nilpotent cone. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-07082013-113917 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3732

Chicago Manual of Style (16^th Edition):

Minn-Thu-Aye, Myron. “Multiplicity formulas for perverse coherent sheaves on the nilpotent cone.” 2013. Doctoral Dissertation, Louisiana State University. Accessed April 13, 2021. etd-07082013-113917 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3732.

MLA Handbook (7^th Edition):

Minn-Thu-Aye, Myron. “Multiplicity formulas for perverse coherent sheaves on the nilpotent cone.” 2013. Web. 13 Apr 2021.

Vancouver:

Minn-Thu-Aye M. Multiplicity formulas for perverse coherent sheaves on the nilpotent cone. [Internet] [Doctoral dissertation]. Louisiana State University; 2013. [cited 2021 Apr 13]. Available from: etd-07082013-113917 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3732.

Council of Science Editors:

Minn-Thu-Aye M. Multiplicity formulas for perverse coherent sheaves on the nilpotent cone. [Doctoral Dissertation]. Louisiana State University; 2013. Available from: etd-07082013-113917 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3732

Louisiana State University

4. Taylor, Sean Michael. Mixed Categories of Sheaves on Toric Varieties.

Degree: PhD, Algebraic Geometry, 2018, Louisiana State University

URL: https://digitalcommons.lsu.edu/gradschool_dissertations/4590

► In [BGS96], Beilinson, Ginzburg, and Soergel introduced the notion of mixed categories. This idea often underlies many interesting "Koszul dualities." In this paper, we… (more)

Subjects/Keywords: Toric varieties; mixed categories; sheaves; finite fields; perverse sheaves; Koszul duality

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Taylor, S. M. (2018). Mixed Categories of Sheaves on Toric Varieties. (Doctoral Dissertation). Louisiana State University. Retrieved from https://digitalcommons.lsu.edu/gradschool_dissertations/4590

Chicago Manual of Style (16^th Edition):

Taylor, Sean Michael. “Mixed Categories of Sheaves on Toric Varieties.” 2018. Doctoral Dissertation, Louisiana State University. Accessed April 13, 2021. https://digitalcommons.lsu.edu/gradschool_dissertations/4590.

MLA Handbook (7^th Edition):

Taylor, Sean Michael. “Mixed Categories of Sheaves on Toric Varieties.” 2018. Web. 13 Apr 2021.

Vancouver:

Taylor SM. Mixed Categories of Sheaves on Toric Varieties. [Internet] [Doctoral dissertation]. Louisiana State University; 2018. [cited 2021 Apr 13]. Available from: https://digitalcommons.lsu.edu/gradschool_dissertations/4590.

Council of Science Editors:

Taylor SM. Mixed Categories of Sheaves on Toric Varieties. [Doctoral Dissertation]. Louisiana State University; 2018. Available from: https://digitalcommons.lsu.edu/gradschool_dissertations/4590

Louisiana State University

5. Matherne, Jacob Paul. Derived Geometric Satake Equivalence, Springer Correspondence, and Small Representations.

Degree: PhD, Applied Mathematics, 2016, Louisiana State University

URL: etd-07022016-000813 ; https://digitalcommons.lsu.edu/gradschool_dissertations/668

► It is known that the geometric Satake equivalence is intimately related to the Springer correspondence when restricting to small representations of the Langlands dual group… (more)

Subjects/Keywords: Geometric Satake; Springer correspondence; small representations; perverse sheaves; algebraic groups

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APA (6^th Edition):

Matherne, J. P. (2016). Derived Geometric Satake Equivalence, Springer Correspondence, and Small Representations. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-07022016-000813 ; https://digitalcommons.lsu.edu/gradschool_dissertations/668

Chicago Manual of Style (16^th Edition):

Matherne, Jacob Paul. “Derived Geometric Satake Equivalence, Springer Correspondence, and Small Representations.” 2016. Doctoral Dissertation, Louisiana State University. Accessed April 13, 2021. etd-07022016-000813 ; https://digitalcommons.lsu.edu/gradschool_dissertations/668.

MLA Handbook (7^th Edition):

Matherne, Jacob Paul. “Derived Geometric Satake Equivalence, Springer Correspondence, and Small Representations.” 2016. Web. 13 Apr 2021.

Vancouver:

Matherne JP. Derived Geometric Satake Equivalence, Springer Correspondence, and Small Representations. [Internet] [Doctoral dissertation]. Louisiana State University; 2016. [cited 2021 Apr 13]. Available from: etd-07022016-000813 ; https://digitalcommons.lsu.edu/gradschool_dissertations/668.

Council of Science Editors:

Matherne JP. Derived Geometric Satake Equivalence, Springer Correspondence, and Small Representations. [Doctoral Dissertation]. Louisiana State University; 2016. Available from: etd-07022016-000813 ; https://digitalcommons.lsu.edu/gradschool_dissertations/668

Louisiana State University

6. Culbertson, Jared Lee. Perverse poisson sheaves on the nilpotent cone.

Degree: PhD, Applied Mathematics, 2010, Louisiana State University

URL: etd-04152010-174523 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3133

► For a reductive complex algebraic group, the associated nilpotent cone is the variety of nilpotent elements in the corresponding Lie algebra. Understanding the nilpotent cone… (more)

Subjects/Keywords: nilpotent cone; Poisson; perverse sheaves

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Culbertson, J. L. (2010). Perverse poisson sheaves on the nilpotent cone. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-04152010-174523 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3133

Chicago Manual of Style (16^th Edition):

Culbertson, Jared Lee. “Perverse poisson sheaves on the nilpotent cone.” 2010. Doctoral Dissertation, Louisiana State University. Accessed April 13, 2021. etd-04152010-174523 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3133.

MLA Handbook (7^th Edition):

Culbertson, Jared Lee. “Perverse poisson sheaves on the nilpotent cone.” 2010. Web. 13 Apr 2021.

Vancouver:

Culbertson JL. Perverse poisson sheaves on the nilpotent cone. [Internet] [Doctoral dissertation]. Louisiana State University; 2010. [cited 2021 Apr 13]. Available from: etd-04152010-174523 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3133.

Council of Science Editors:

Culbertson JL. Perverse poisson sheaves on the nilpotent cone. [Doctoral Dissertation]. Louisiana State University; 2010. Available from: etd-04152010-174523 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3133

University of California – Berkeley

7. Jin, Xin. Symplectic approaches in geometric representation theory.

Degree: Mathematics, 2015, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/07t5s31b

► We study various topics lying in the crossroads of symplectic topology and geometric representation theory, with an emphasis on understanding central objects in geometric representation… (more)

Subjects/Keywords: Mathematics; Fukaya categories; geometric representation theory; Lagrangian branes; perverse sheaves; symplectic geometry; symplectomorphism groups

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APA (6^th Edition):

Jin, X. (2015). Symplectic approaches in geometric representation theory. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/07t5s31b

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Jin, Xin. “Symplectic approaches in geometric representation theory.” 2015. Thesis, University of California – Berkeley. Accessed April 13, 2021. http://www.escholarship.org/uc/item/07t5s31b.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Jin, Xin. “Symplectic approaches in geometric representation theory.” 2015. Web. 13 Apr 2021.

Vancouver:

Jin X. Symplectic approaches in geometric representation theory. [Internet] [Thesis]. University of California – Berkeley; 2015. [cited 2021 Apr 13]. Available from: http://www.escholarship.org/uc/item/07t5s31b.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Jin X. Symplectic approaches in geometric representation theory. [Thesis]. University of California – Berkeley; 2015. Available from: http://www.escholarship.org/uc/item/07t5s31b

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

8. Hepler, Brian. Hypersurface Normalizations And Numerical Invariants.

Degree: PhD, Department of Mathematics, 2019, Northeastern University

URL: http://hdl.handle.net/2047/D20316378

► We define a new perverse sheaf, the comparison complex, naturally associated to any locally reduced complex analytic space X on which the (shifted) constant sheaf… (more)

Subjects/Keywords: Algebraic Geometry; Hodge Theory; Perverse Sheaves; Singularities; Mathematics

…approach using perverse sheaves allows us to make some headway. Particularly, these spaces are… …short exact sequence of perverse sheaves on X, and Theorem 1.1.1.4, which is our main… …extension of semi-simple perverse sheaves?” This question was posed to us by a referee of [21… …surjection of perverse sheaves Z•X [n] → I•X → 0, where I•X is the intersection… …simple object in the category of perverse sheaves on X with no perverse sub or quotient objects…

2 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hepler, B. (2019). Hypersurface Normalizations And Numerical Invariants. (Doctoral Dissertation). Northeastern University. Retrieved from http://hdl.handle.net/2047/D20316378

Chicago Manual of Style (16^th Edition):

Hepler, Brian. “Hypersurface Normalizations And Numerical Invariants.” 2019. Doctoral Dissertation, Northeastern University. Accessed April 13, 2021. http://hdl.handle.net/2047/D20316378.

MLA Handbook (7^th Edition):

Hepler, Brian. “Hypersurface Normalizations And Numerical Invariants.” 2019. Web. 13 Apr 2021.

Vancouver:

Hepler B. Hypersurface Normalizations And Numerical Invariants. [Internet] [Doctoral dissertation]. Northeastern University; 2019. [cited 2021 Apr 13]. Available from: http://hdl.handle.net/2047/D20316378.

Council of Science Editors:

Hepler B. Hypersurface Normalizations And Numerical Invariants. [Doctoral Dissertation]. Northeastern University; 2019. Available from: http://hdl.handle.net/2047/D20316378

University of Texas – Austin

9. Mautner, Carl Irving. Sheaf theoretic methods in modular representation theory.

Degree: PhD, Mathematics, 2010, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2010-05-943

► This thesis concerns the use of perverse sheaves with coefficients in commutative rings and in particular, fields of positive characteristic, in the study of modular… (more)

Subjects/Keywords: Perverse sheaves; Modular representation theory; Schur-Weyl duality; Parity sheaves; Sheaf theoretic methods; Commutative rings; Decomposition theorem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mautner, C. I. (2010). Sheaf theoretic methods in modular representation theory. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2010-05-943

Chicago Manual of Style (16^th Edition):

Mautner, Carl Irving. “Sheaf theoretic methods in modular representation theory.” 2010. Doctoral Dissertation, University of Texas – Austin. Accessed April 13, 2021. http://hdl.handle.net/2152/ETD-UT-2010-05-943.

MLA Handbook (7^th Edition):

Mautner, Carl Irving. “Sheaf theoretic methods in modular representation theory.” 2010. Web. 13 Apr 2021.

Vancouver:

Mautner CI. Sheaf theoretic methods in modular representation theory. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2010. [cited 2021 Apr 13]. Available from: http://hdl.handle.net/2152/ETD-UT-2010-05-943.

Council of Science Editors:

Mautner CI. Sheaf theoretic methods in modular representation theory. [Doctoral Dissertation]. University of Texas – Austin; 2010. Available from: http://hdl.handle.net/2152/ETD-UT-2010-05-943

10. Kochersperger, Matthieu. Cycles proches, cycles évanescents et théorie de Hodge pour les morphismes sans pente : Nearby cycles, vanishing cycles and Hodge theory for morphisms without slope.

Degree: Docteur es, Mathématiques fondamentales, 2018, Université Paris-Saclay (ComUE)

URL: http://www.theses.fr/2018SACLX041

►

Dans cette thèse nous nous intéressons aux singularités d'espaces analytiques complexes définis comme le lieu des zéros d'un morphisme sans pente. Nous étudions dans un… (more)

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Dans cette thèse nous nous intéressons aux singularités d'espaces analytiques complexes définis comme le lieu des zéros d'un morphisme sans pente. Nous étudions dans un premier temps les cycles proches et les cycles évanescents associés à un tel morphisme. Dans un deuxième temps nous cherchons à comprendre la théorie de Hodge des morphismes sans pente.La première partie de cette thèse est consacrée à apporter des compléments au travail de P. Maisonobe sur les morphismes sans pente. Nous commençons par construire un morphisme de comparaison entre cycles proches algébriques (pour les D-modules) et cycles proches topologiques (pour les faisceaux pervers). Nous montrons ensuite que ce morphisme est un isomorphisme dans le cas d'un morphisme sans pente. Enfin nous construisons un foncteur cycles évanescents topologiques pour un morphisme sans pente et nous démontrons que ce foncteur et le foncteur cycles proches topologiques de P. Maisonobe se placent dans le diagramme de triangles exacts attendu.Dans la seconde partie de cette thèse nous étudions les morphismes sans pente pour les modules de Hodge mixtes. Nous démontrons dans un premier temps la commutativité des cycles proches et des cycles évanescents itérés appliqués à un module de Hodge mixte dans le cas d'un morphisme sans pente. Dans un deuxième temps nous définissons la notion "strictement sans pente" pour un module de Hodge mixte et nous démontrons sa stabilité par image directe propre. Nous démontrons comme application la compatibilité de la filtration de Hodge et des filtrations de Kashiwara-Malgrange pour certains modules de Hodge purs supportés sur une hypersurface à singularités quasi-ordinaires.

In this thesis we are interested in singularities of complex varieties defined as the zero locus of a morphism without slope. In a first time we study nearby cycles and vanishing cycles associated to such morphisms. In a second time we want to understand Hodge theory of morphisms without slope.The first part of this thesis is devoted to add some complements to the work of P. Maisonobe on morphisms without slope. We start with the construction of a comparison morphism between algebraic nearby cycles (for D-modules) and topological nearby cycles (for perverse sheaves). Then we show that this morphism is an isomorphism in the case of a morphism without slope. Finally we construct a topological vanishing cycles functor for a morphism without slope et we prove that this functor and the topological nearby cycles functor of P. Maisonobe fit into the expected diagram of exact triangles.In the second part of the thesis we study morphisms without slope for mixed Hodge modules. We first show the commutativity of iterated nearby cycles and vanishing cycles applied to a mixed Hodge module in the case of a morphism without slope. Second we define the notion "strictly without slope" for a mixed Hodge module and we show that it is preserved by proper direct image. As an application we prove the compatibility of the Hodge filtration and Kashiwara-Malgrange filtrations for some…

Advisors/Committee Members: Sabbah, Claude (thesis director).

Subjects/Keywords: Morphisme sans pente; Cycles évanescents; Multifiltration de Kashiwara-Malgrange; Modules de Hodge mixtes; D-Modules; Faisceaux pervers; Cycles proches; Morphisms without slope; Vanishing cycles; Kashiwara-Malgrange multifiltration; Mixed Hodge modules; D-Modules; Perverse sheaves; Nearby cycles; 514.74

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kochersperger, M. (2018). Cycles proches, cycles évanescents et théorie de Hodge pour les morphismes sans pente : Nearby cycles, vanishing cycles and Hodge theory for morphisms without slope. (Doctoral Dissertation). Université Paris-Saclay (ComUE). Retrieved from http://www.theses.fr/2018SACLX041

Chicago Manual of Style (16^th Edition):

Kochersperger, Matthieu. “Cycles proches, cycles évanescents et théorie de Hodge pour les morphismes sans pente : Nearby cycles, vanishing cycles and Hodge theory for morphisms without slope.” 2018. Doctoral Dissertation, Université Paris-Saclay (ComUE). Accessed April 13, 2021. http://www.theses.fr/2018SACLX041.

MLA Handbook (7^th Edition):

Kochersperger, Matthieu. “Cycles proches, cycles évanescents et théorie de Hodge pour les morphismes sans pente : Nearby cycles, vanishing cycles and Hodge theory for morphisms without slope.” 2018. Web. 13 Apr 2021.

Vancouver:

Kochersperger M. Cycles proches, cycles évanescents et théorie de Hodge pour les morphismes sans pente : Nearby cycles, vanishing cycles and Hodge theory for morphisms without slope. [Internet] [Doctoral dissertation]. Université Paris-Saclay (ComUE); 2018. [cited 2021 Apr 13]. Available from: http://www.theses.fr/2018SACLX041.

Council of Science Editors:

Kochersperger M. Cycles proches, cycles évanescents et théorie de Hodge pour les morphismes sans pente : Nearby cycles, vanishing cycles and Hodge theory for morphisms without slope. [Doctoral Dissertation]. Université Paris-Saclay (ComUE); 2018. Available from: http://www.theses.fr/2018SACLX041

Open Access Theses and Dissertations