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

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University of Illinois – Chicago

1. Lombardi, Luigi. Derived Equivalences of Irregular Varieties and Constraints on Hodge Numbers.

Degree: 2013, University of Illinois – Chicago

We study derived equivalences of smooth projective irregular varieties. More specifically, as suggested by a conjecture of Popa, we investigate the behavior of cohomological support loci associated to the canonical bundle (around the origin) under derived equivalence. We approach this problem in two ways. In the first approach we establish and apply the derived invariance of a ``twisted'' version of Hochschild homology taking into account an isomorphism due to Rouquier and related to autoequivalences of derived categories. In the second approach we relate the derived invariance of cohomological support loci to the derived invariance of Hodge numbers. As a result, we obtain the derived invariance of the first two and the last two cohomological support loci, leading to interesting geometric applications. For instance, we deduce the derived invariance of a few numerical quantities attached to irregular varieties, and furthermore we describe the geometry of Fourier-Mukai partners of Fano fibrations, and hence of Mori fiber spaces, fibered over curves of genus at least two. Finally, we also study constraints on Hodge numbers of special classes of irregular compact Kaehler manifolds. More specifically, we write down nequalities for all the Hodge numbers by studying the exactness of BGG complexes associated to bundles of holomorphic p-forms and by using classical results in the theory of vector bundles on projective spaces. As an application of our techniques, we bound the regularity of cohomology modules in terms of the defect of semismallness of the Albanese map. Advisors/Committee Members: Popa, Mihnea (advisor), Budur, Nero (committee member), Coskun, Izzet (committee member), Ein, Lawrence (committee member), Libgober, Anatoly (committee member).

Subjects/Keywords: Derived Categories; Equivalences; Non-vanishing Loci; Irregular Varieties; Picard Variety; Hodge Numbers; Derivative Complex; Hochschild homology

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

APA (6th Edition):

Lombardi, L. (2013). Derived Equivalences of Irregular Varieties and Constraints on Hodge Numbers. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/10294

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):

Lombardi, Luigi. “Derived Equivalences of Irregular Varieties and Constraints on Hodge Numbers.” 2013. Thesis, University of Illinois – Chicago. Accessed July 12, 2020. http://hdl.handle.net/10027/10294.

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

MLA Handbook (7th Edition):

Lombardi, Luigi. “Derived Equivalences of Irregular Varieties and Constraints on Hodge Numbers.” 2013. Web. 12 Jul 2020.

Vancouver:

Lombardi L. Derived Equivalences of Irregular Varieties and Constraints on Hodge Numbers. [Internet] [Thesis]. University of Illinois – Chicago; 2013. [cited 2020 Jul 12]. Available from: http://hdl.handle.net/10027/10294.

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

Council of Science Editors:

Lombardi L. Derived Equivalences of Irregular Varieties and Constraints on Hodge Numbers. [Thesis]. University of Illinois – Chicago; 2013. Available from: http://hdl.handle.net/10027/10294

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


Université de Bordeaux I

2. Laurent, Arthur. Autour des nombres de Tamagawa : On Tamagawa Numbers.

Degree: Docteur es, Mathématiques pures, 2013, Université de Bordeaux I

Les nombres de Tamagawa des courbes elliptiques apparaissent dans la formulation de la conjecture de Birch et Swinnerton-Dyer comme certains facteurs locaux. Bloch et Kato (1990) ont trouvé une vaste généralisation de cette définition classique en termes de la théorie de Hodge p-adique. Ils ont associé un nombre de Tamagawa Tam(T) à tout réseau T de représentations p-adiques de de Rham au sens de J.-M. Fontaine. Ces nombres interviennent dans les conjectures de Bloch et Kato sur les valeurs spéciales des fonctions L des motifs.J.-M. Fontaine et B.Perrin-Riou ont formulé une conjecture reliant Tam(T) et le nombre de Tamagawa Tam(T*}(1)) de la représentation duale. Cette conjecture est connue pour les représentations cristallines ce qui permet de calculer explicitement les nombres de Tamagawa des représentations cristallines dont les poids de Hodge-Tate sont tous positifs. En revanche, dans la plupart des autres cas, nous n'avons pas de méthode de calcul explicite. Cette thèse a pour but de donner un encadrement des nombres de Tamagawa des représentations absolument cristallines le long de la tour cyclotomique sans hypothèses supplémentaires sur les poids de Hodge-Tate. Le premier chapitre de cette thèse est dédié à des rappels sur la théorie de Hodge p-adique, la classification de Fontaine des représentations p-adique de corps locaux via la théorie des (phi, Gamma)-modules, sur la cohomologie galoisienne, sur les modules de Wach ou sur la cohomologie d'Iwasawa. Le second chapitre est dédié à l'exponentielle de Bloch and Kato. Seront rappelées sa définition et sa construction de l'exponentielle de Bloch and Kato en termes de (phi, Gamma)-modules faite par D.Benois. Cette dernière construction permet de généraliser deux résultats de D.Benois et L.Berger qui relient l'exponentielle aux modules de Wach et qui permet de décrire des objets qui apparaissent naturellement dans l'étude des nombres de Tamagawa. Le dernier chapitre est le cœur de cette thèse. Nous commencerons en définissant les nombres de Tamagawa Tam(T) et en donnant certaines propriétés et résultats déjà connus. Nous énonçons ensuite le théorème final qui donne un encadrement des nombres de Tamagawa d'une représentation absolument cristalline V. Y sont également donnés certains cas d'égalité qui permettent de retrouver des formules connues  – lorsque V est positive ou lorsqu'elle provient d'une courbe elliptique et plus généralement d'un groupe formel de dimension 1 et de hauteur 2. Pour prouver ces résultats, nous écrivons les nombres de Tamagawa sous forme d'un indice généralisé dans lequel apparaissent les objets étudiés dans le chapitre précédent. La thèse se termine avec l'étude de plusieurs cas particuliers qui permettent de retrouver des résultats déjà connus.

Tamagawa numbers of elliptic curves appear in the Birch and Swinnerton-Dyer conjecture as local factors. Bloch and Kato generalized the definition using p-adic Hodge theory in 1990. Indeed they associated a number Tam(T) to each lattice T of de Rham representation in the sense of…

Advisors/Committee Members: Benois, Denis (thesis director).

Subjects/Keywords: Théorie de hodge p-adique; Exponentielle de Bloch et Kato; Nombres de Tamagawa; Théorie des (Phi, Gamma)-modules; Modules de Wach; P-adic Hodge theory; Bloch and Kato's exponential map; Tamagawa numbers; (Phi, Gamma)-modules theory; Wach modules

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

APA (6th Edition):

Laurent, A. (2013). Autour des nombres de Tamagawa : On Tamagawa Numbers. (Doctoral Dissertation). Université de Bordeaux I. Retrieved from http://www.theses.fr/2013BOR14809

Chicago Manual of Style (16th Edition):

Laurent, Arthur. “Autour des nombres de Tamagawa : On Tamagawa Numbers.” 2013. Doctoral Dissertation, Université de Bordeaux I. Accessed July 12, 2020. http://www.theses.fr/2013BOR14809.

MLA Handbook (7th Edition):

Laurent, Arthur. “Autour des nombres de Tamagawa : On Tamagawa Numbers.” 2013. Web. 12 Jul 2020.

Vancouver:

Laurent A. Autour des nombres de Tamagawa : On Tamagawa Numbers. [Internet] [Doctoral dissertation]. Université de Bordeaux I; 2013. [cited 2020 Jul 12]. Available from: http://www.theses.fr/2013BOR14809.

Council of Science Editors:

Laurent A. Autour des nombres de Tamagawa : On Tamagawa Numbers. [Doctoral Dissertation]. Université de Bordeaux I; 2013. Available from: http://www.theses.fr/2013BOR14809

3. Kang, Jinwoo. Two Views on Gravity: F-Theory and Holography.

Degree: PhD, 2019, Harvard University

We investigate two different views towards gravitational theories using mathematical frameworks. First, we study gravitational theories with supersymmetries in various dimensions from top-down approach via F-theory or M-theory compactifications. We utilize the geometry of elliptic fibrations to investigate such compactifications. The other viewpoint does not require to study theories with supersymmetries. With the framework of von Neumann algebras, we study gravitational theories in the bulk and its boundary conformal field theories. We consider the construction of supergravity theories in three to six dimensions via the compactifcation of M-theory and F-theory on elliptically-fibered manifolds. Interesting gauge theory sectors arise when such manifolds have singularities. We study the resolutions of singularities of these spaces which give the window onto the low energy physics of effective supergravity. We consider elliptically-fibered Calabi – Yau threefolds that give rise to supergravities with simple gauge groups, with a particular emphasis on F4, G2, Spin(7), and Spin(8), or semi-simple gauge groups of the form SO(4), Spin(4), \sug , \susu , \susp , \susp /ℤ2, \susuf , and \susuf /ℤ2. For such models we enumerate the spectra in five-dimensions and six-dimensions with eight supercharges via M-theory and F-theory compactifications and determine the structure of the Coulomb branch for these 5d theories. Furthermore we verify that all local anomalies in 6d are canceled. For theories with an abelian gauge group we introduced a new, general model for an elliptic fibration that realizes this U(1) symmetry. The physical spectra often depends on topological invariants of the elliptic fibration. In particular, when the effective theory is required to be supersymmetric, the elliptic fibration must be Calabi – Yau. In the more general case, when the fibration is not assumed to be Calabi – Yau, we utilized the resolution of singularities to determine a host of topological invariants and characteristic numbers for elliptic fibrations that correspond to a physical gauge group with a simple non-abelian factor. These include the Euler characteristic, Hodge numbers, Chern numbers, Pontryagin numbers, Todd genus, holomorphic genera, L-genus, A-genus, and the M-theory curvature invariant. In a different vein, infinite-dimensional von Neumann algebras of various types are used to understand the local algebras in quantum field theories. Utilizing such von Neumann algebras, one can study holographic quantum field theories and their gravity duals by incorporating toy models from quantum error correction. We reformulate the entanglement wedge reconstruction in the language of infinite-dimensional von Neumann algebras. Using the frame of Tomita – Takasaki theory, we can also write the infinite-dimensional analog of the relative entropies. Using these techniques, we show that for a general infinite-dimensional Hilbert space, the entanglement wedge reconstruction is identical to the equivalence in… Advisors/Committee Members: Jafferis, Daniel (advisor), Esole, Jonathan Mboyo (committee member), Franklin, Melissa (committee member), Strominger, Andy (committee member).

Subjects/Keywords: Elliptic fibrations; resolutions of singularities; flop transitions; Weierstrass model; Tate’s algorithm; six-dimensional supergravity; five-dimensional supergravity; anomaly cancellation; Euler characteristic; F-Theory; M-Theory; gauge theory; singularity; Calabi-Yau; minimal model; Mordell-Weil group; Coulomb chambers; Hodge numbers; Characteristic numbers; holography; entanglement entropy; infinite-dimensional Hilbert space; von Neumann algebra; modular operator; tensor network; quantum error correcting code

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

APA (6th Edition):

Kang, J. (2019). Two Views on Gravity: F-Theory and Holography. (Doctoral Dissertation). Harvard University. Retrieved from http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029691

Chicago Manual of Style (16th Edition):

Kang, Jinwoo. “Two Views on Gravity: F-Theory and Holography.” 2019. Doctoral Dissertation, Harvard University. Accessed July 12, 2020. http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029691.

MLA Handbook (7th Edition):

Kang, Jinwoo. “Two Views on Gravity: F-Theory and Holography.” 2019. Web. 12 Jul 2020.

Vancouver:

Kang J. Two Views on Gravity: F-Theory and Holography. [Internet] [Doctoral dissertation]. Harvard University; 2019. [cited 2020 Jul 12]. Available from: http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029691.

Council of Science Editors:

Kang J. Two Views on Gravity: F-Theory and Holography. [Doctoral Dissertation]. Harvard University; 2019. Available from: http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029691

.