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Abstracts for Oberseminar Arithmetische Geometrie und Darstellungstheorie

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Some recent advances on the $p$-adic Hodge theory of integral models of Shimura varieties

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Speaker: 
Alex Youcis
Affiliation: 
National University of Singapore
Date: 
Fri, 19/04/2024 - 14:05 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Oberseminar Arithmetische Geometrie und Darstellungstheorie

The geometry of Shimura varieties has played a central role in the development of, and progress in, the Langlands program. Complicating the study of these objects is the lack of moduli interpretations of general Shimura varieties which ought to involve the theory of motives -- a theory that remains largely conjectural.

D-modules on the Fargues-Fontaine curve

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Speaker: 
Guido Bosco
Affiliation: 
MPIM
Date: 
Fri, 26/04/2024 - 14:05 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Oberseminar Arithmetische Geometrie und Darstellungstheorie

Circling the categorical local Langlands conjecture

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Speaker: 
David Hansen
Affiliation: 
National University of Singapore
Date: 
Fri, 10/05/2024 - 14:05 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Oberseminar Arithmetische Geometrie und Darstellungstheorie

Nilpotent orbits and Cartan subalgebras in reductive p-adic groups

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Speaker: 
Stephen DeBacker
Affiliation: 
University of Michigan
Date: 
Fri, 07/06/2024 - 14:05 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Oberseminar Arithmetische Geometrie und Darstellungstheorie
Details: 
Program and Abstracts of Nilpotent orbits and Cartan subalgebras in reductive p-adic groups

For real Lie groups, complex Lie groups, and finite groups of Lie type we have had a very good understanding of both the set of nilpotent orbits and the set of conjugacy classes of Cartan subalgebras for at least half a century.  In this talk I will describe and illustrate a way to understand these objects for reductive p-adic groups.

 

Categorical local Langlands on isocrystals

Posted in
Speaker: 
Arnaud Eteve
Affiliation: 
MPIM
Date: 
Fri, 21/06/2024 - 14:05 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Oberseminar Arithmetische Geometrie und Darstellungstheorie

(jt with D. Gaistgory, A. Genestier and V. Lafforgue) Let F be a local field of equal characteristic and G be a reductive group over F. The conjectural categorical form of the local Langlands correspondence proposed by Fargues and Scholze is an equivalence of categories between on one side the category of $\ell$-adic sheaves on $\Bun_G(X_{FF})$ the stack of $G$-torsors on the Fargues-Fontaine curve and and on the other side the category of coherent sheaves on the stack of $L$-parameters.

 

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