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You searched for subject:(Koszul homology). Showing records 1 – 3 of 3 total matches.

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University of Michigan

1. Klein, Patricia. Relationships Among Hilbert-Samuel Multiplicities, Koszul Cohomology, and Local Cohomology.

Degree: PhD, Mathematics, 2018, University of Michigan

We consider relationships among Hilbert-Samuel multiplicities, Koszul cohomology, and local cohomology. In particular, we investigate upper and lower bounds on the ratio e(I,M)/l(M/IM) for m-primary ideals I of the local ring (R,m) and finitely generated quasi-unmixed R-modules M and, in joint work with Linquan Ma, Pham Hung Quy, Ilya Smirnov, and Yongwei Yao, give a precise formula for the upper bound for all finitely-generated R-modules M and show that the ratio is bounded away from 0 whenever M is quasi-unmixed. We also, as independent work, give a characterization of quasi-unmixed R-modules M whose local cohomology is finite length up to some index in terms of asymptotic vanishing of Koszul cohomology on parameter ideals up to the same index. We show that if M is an equidimensional module over a complete local ring, then M is asymptotically Cohen-Macaulay if and only if the supremum of the set of lengths of lower Koszul cohomology modules on systems of parameters if finite if and only if M is Cohen-Macaulay on the punctured spectrum. Advisors/Committee Members: Hochster, Mel (committee member), Goldberg, Deborah E (committee member), Gunturkun, Sema (committee member), Ho, Wei (committee member), Smith, Karen E (committee member).

Subjects/Keywords: commutative algebra; homological algebra; Hilbert-Samuel multiplicities; Koszul homology; Lech's inequality; Mathematics; Science

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APA (6th Edition):

Klein, P. (2018). Relationships Among Hilbert-Samuel Multiplicities, Koszul Cohomology, and Local Cohomology. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/145974

Chicago Manual of Style (16th Edition):

Klein, Patricia. “Relationships Among Hilbert-Samuel Multiplicities, Koszul Cohomology, and Local Cohomology.” 2018. Doctoral Dissertation, University of Michigan. Accessed July 15, 2020. http://hdl.handle.net/2027.42/145974.

MLA Handbook (7th Edition):

Klein, Patricia. “Relationships Among Hilbert-Samuel Multiplicities, Koszul Cohomology, and Local Cohomology.” 2018. Web. 15 Jul 2020.

Vancouver:

Klein P. Relationships Among Hilbert-Samuel Multiplicities, Koszul Cohomology, and Local Cohomology. [Internet] [Doctoral dissertation]. University of Michigan; 2018. [cited 2020 Jul 15]. Available from: http://hdl.handle.net/2027.42/145974.

Council of Science Editors:

Klein P. Relationships Among Hilbert-Samuel Multiplicities, Koszul Cohomology, and Local Cohomology. [Doctoral Dissertation]. University of Michigan; 2018. Available from: http://hdl.handle.net/2027.42/145974


Harvard University

2. Brantner, David Lukas Benjamin. The Lubin-Tate Theory of Spectral Lie Algebras.

Degree: PhD, 2017, Harvard University

We use equivariant discrete Morse theory to establish a general technique in poset topology and demonstrate its applicability by computing various equivariant properties of the partition complex and related posets in a uniform manner. Our technique gives new and purely combinatorial proofs of results on algebraic and topological André-Quillen homology. We then carry out a general study of the relation between monadic Koszul duality and unstable power operations. Finally, we combine our techniques to compute the operations which act on the homotopy groups K(n)-local Lie algebras over Lubin-Tate space.

Mathematics

Advisors/Committee Members: Lurie, Jacob A. (advisor), Hopkins, Michael J. (committee member), Arone, Gregory Z. (committee member).

Subjects/Keywords: Morava E-theory; Lubin-Tate space; spectral Lie algebras; poset topology; discrete Morse theory; Andre-Quillen homology; monoids; Koszul duality

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

APA (6th Edition):

Brantner, D. L. B. (2017). The Lubin-Tate Theory of Spectral Lie Algebras. (Doctoral Dissertation). Harvard University. Retrieved from http://nrs.harvard.edu/urn-3:HUL.InstRepos:41140243

Chicago Manual of Style (16th Edition):

Brantner, David Lukas Benjamin. “The Lubin-Tate Theory of Spectral Lie Algebras.” 2017. Doctoral Dissertation, Harvard University. Accessed July 15, 2020. http://nrs.harvard.edu/urn-3:HUL.InstRepos:41140243.

MLA Handbook (7th Edition):

Brantner, David Lukas Benjamin. “The Lubin-Tate Theory of Spectral Lie Algebras.” 2017. Web. 15 Jul 2020.

Vancouver:

Brantner DLB. The Lubin-Tate Theory of Spectral Lie Algebras. [Internet] [Doctoral dissertation]. Harvard University; 2017. [cited 2020 Jul 15]. Available from: http://nrs.harvard.edu/urn-3:HUL.InstRepos:41140243.

Council of Science Editors:

Brantner DLB. The Lubin-Tate Theory of Spectral Lie Algebras. [Doctoral Dissertation]. Harvard University; 2017. Available from: http://nrs.harvard.edu/urn-3:HUL.InstRepos:41140243

3. Sáenz de Cabezón Irigaray, Eduardo. Combinatorial Koszul Homology: Computations and Applications = Homología de Koszul combinatoria: Cálculos y aplicaciones.

Degree: 2008, Universidad de La Rioja

With a particular focus on explicit computations and applications of the Koszul homology and Betti numbers of monomial ideals, the main goals od this thesis are the following: Analyze the Koszul homology of monomial ideals and apply it to describe the structure of monomial ideals. Describe algorithms to perform efficient computations of the homological invariants of monomial ideals. Apply the theory and computations on monomial ideals to problems inside and outside mathematics. The thesis introduces as a main tool Mayer-Vietoris trees of monomial ideals.

Esta tesis está centrada en cálculos explícitos y aplicaciones de la homología de Koszul y los números de Betti de ideales monomiales. Con este interés presente, los objetivos principales son: - Analizar la homología de Koszul de ideales monomiales y aplicarla a la descripción de la estructura de dichos ideales. - Describir algoritmos para realizar cálculos eficaces de los invariantes homológicos de ideales de monomios, en particular en números de Betti, resoluciones libres, homología de Koszul y serie de Hilbert. - Aplicar la teoría de ideales monomiales a problemas dentro y fuera de las matemáticas, haciendo uso, en particular, de los invariantes homológicos de estos ideales.

Advisors/Committee Members: Hernández Paricio, Luis Javier (Universidad de La Rioja), Seiler, Werner M. (Universität Mannheim).

Subjects/Keywords: combinatorial commutative algebra; monomial ideals; Betti numbers; algebraic analysis of system reliability; formal theory of differential systems; homología de Koszul; álgebra conmutativa combinatoria; ideales monomiales; números de Betti; análisis algebráico de la fiabilidad de sistemas; teoría formal de sistemas diferenciales; Koszul homology

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

APA (6th Edition):

Sáenz de Cabezón Irigaray, E. (2008). Combinatorial Koszul Homology: Computations and Applications = Homología de Koszul combinatoria: Cálculos y aplicaciones. (Thesis). Universidad de La Rioja. Retrieved from https://dialnet.unirioja.es/servlet/oaites?codigo=13745

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

Chicago Manual of Style (16th Edition):

Sáenz de Cabezón Irigaray, Eduardo. “Combinatorial Koszul Homology: Computations and Applications = Homología de Koszul combinatoria: Cálculos y aplicaciones.” 2008. Thesis, Universidad de La Rioja. Accessed July 15, 2020. https://dialnet.unirioja.es/servlet/oaites?codigo=13745.

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

MLA Handbook (7th Edition):

Sáenz de Cabezón Irigaray, Eduardo. “Combinatorial Koszul Homology: Computations and Applications = Homología de Koszul combinatoria: Cálculos y aplicaciones.” 2008. Web. 15 Jul 2020.

Vancouver:

Sáenz de Cabezón Irigaray E. Combinatorial Koszul Homology: Computations and Applications = Homología de Koszul combinatoria: Cálculos y aplicaciones. [Internet] [Thesis]. Universidad de La Rioja; 2008. [cited 2020 Jul 15]. Available from: https://dialnet.unirioja.es/servlet/oaites?codigo=13745.

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

Council of Science Editors:

Sáenz de Cabezón Irigaray E. Combinatorial Koszul Homology: Computations and Applications = Homología de Koszul combinatoria: Cálculos y aplicaciones. [Thesis]. Universidad de La Rioja; 2008. Available from: https://dialnet.unirioja.es/servlet/oaites?codigo=13745

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

.