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#Shimura Varieties

Showing: 15 courses
Institute for Advanced Study

Independence of ℓ for Frobenius Conjugacy Classes Attached to Abelian Varieties - Rong Zhou

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Explore Frobenius conjugacy classes in abelian varieties, focusing on independence of ℓ, Mumford-Tate groups, and connections to Shimura varieties and CM liftings.
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14 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Hidden Symmetries of the Work of Jan Nekovář

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Explorez les principes unificateurs de la recherche de Jan Nekovar, des systèmes d'Euler aux variétés de Shimura quaternioniques, en passant par les résultats de parité pour les fonctions L.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
IMSA

Fixed Points in Toroidal Compactifications and Essential Dimension of Covers

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Explores essential dimension in algebraic objects, focusing on congruence covers of Shimura varieties. Presents new geometric approaches and fixed point theorems, extending incompressibility results to exceptional types.
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14 Lesons
57 minutes
On-Demand
Free-Video
Fields Institute

Foliations on Shimura Varieties

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Explore foliations on Shimura varieties, focusing on inseparable morphisms, characteristic P, and applications to surfaces and general cases in algebraic geometry.
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11 Lesons
1 hour 20 minutes
On-Demand
Free-Video
International Mathematical Union

The Cohomology of Shimura Varieties with Torsion Coefficients and Applications

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Explore Shimura varieties' cohomology with torsion coefficients and its applications in advanced mathematics, presented by Ana Caraiani.
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1 Lesons
41 minutes
On-Demand
Free-Video
International Mathematical Union

Points on Shimura Varieties Modulo Primes

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Explore the intricacies of Shimura varieties modulo primes, delving into advanced mathematical concepts and their applications in number theory and algebraic geometry.
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1 Lesons
47 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Geometric Eisenstein Series and Torsion Vanishing

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Explores torsion vanishing in cohomology of Shimura varieties, combining geometric Eisenstein series, Fargues-Scholze local Langlands correspondence, and Hecke correspondences to extend previous results.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

On Exotic Hecke Correspondences

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Explores construction of exotic Hecke correspondences between mod p-fibers of different Shimura varieties, generalizing Xiao-Zhu's work and allowing non-isomorphic groups at p, leading to exotic Igusa variety isomorphisms.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

An Introduction to Geometric Sen Theory

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Explore geometric Sen theory, its applications to Shimura varieties, and connections with proétale cohomology. Learn about solid locally analytic representations and perfectoid Shimura varieties.
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1 Lesons
1 hour 58 minutes
On-Demand
Free-Video
Fields Institute

Integral Canonical Models of Exceptional Shimura Varieties

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Explore advanced mathematical concepts in exceptional Shimura varieties and their integral canonical models, presented by Jacob Tsimerman from the University of Toronto.
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1 Lesons
33 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Zeta Functions of Shimura Varieties: Past, Present, and the Near Future

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Explore Zeta functions of Shimura varieties, covering historical developments, current research, and future directions in this advanced mathematical topic.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Shimurian Analogs of Barsotti-Tate Groups

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Explore Grothendieck's n-truncated Barsotti-Tate groups and their modulo p reductions. Discover conjectures on Shimura varieties and modern Dieudonné theory developments.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Period Relations for Arithmetic Automorphic Periods on Unitary Groups

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Explore period relations for arithmetic automorphic periods on unitary groups, focusing on Petersson inner products and connections to L-function special values.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

On the Cohomology of Shimura Varieties with Torsion Coefficients

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Explore recent advances in Shimura varieties' cohomology with torsion coefficients, including Hodge-Tate period morphism geometry and local-global compatibility insights.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Fields Institute

On Normalization in the Integral Models of Shimura Varieties of Hodge Type

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Explore normalization in integral models of Shimura varieties of Hodge type, delving into advanced number theory concepts and their applications in algebraic geometry.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video