Session S21 - Galois representations and automorphic forms

Tuesday, July 13, 14:30 ~ 15:10 UTC-3

Drinfeld's lemma for $F$-isocrystals

Kiran S. Kedlaya

University of California San Diego, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Drinfeld's lemma on the fundamental groups of schemes in characteristic $p>0$ plays a fundamental role in the construction of the "automorphic to Galois" Langlands correspondence in positive characteristic, as in the work of V. Lafforgue. We describe a corresponding statement in which the roles of lisse etale sheaves and constructible sheaves are instead played by overconvergent $F$-isocrystals and arithmetic $\mathcal{D}$-modules, which is needed in order to transpose Lafforgue's argument to $p$-adic coefficients.

Joint work with Daxin Xu (Morningside Center of Mathematics).

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