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Algebra and Geometry Seminar

Monday, October 25, 2021
4:00pm to 5:00pm
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Linde Hall 387
p-adic analogues of Drinfeld's lemma
Kiran Kedlaya, Department of Mathematics, UC San Diego,

Drinfeld's lemma for an F_p-scheme X asserts a close relationship between X and the formal categorical quotient of the product of X with an algebraically closed field divided by the "partial Frobenius" action on the second factor. In particular, Drinfeld shows that these two have the same lisse and constructible etale sheaves.

We describe two different p-adic analogues of this result, both of which have implications for the Langlands correspondence. One is for lisse sheaves on perfectoid spaces and is related to the Fargues-Scholze construction for mixed-characteristic local Langlands; it also gives rise to a multivariate analogue of (phi, Gamma)-module theory for representations of powers of a local Galois group (the latter being joint work with Annie Carter and Gergely Zabradi). The other is for F-isocrystals and D-modules (joint work with Daxin Xu), and is needed for a crystalline analogue of V. Lafforgue's approach to geometric Langlands for reductive groups (parallel to Abe's crystalline analogue of L. Lafforgue's theorem for GL(n)).

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.