## View abstract

### 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. document.getElementById('cloak6e92399515cfeb1ca5ccf169a0a6dd6a').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy6e92399515cfeb1ca5ccf169a0a6dd6a = 'k&#101;dl&#97;y&#97;' + '&#64;'; addy6e92399515cfeb1ca5ccf169a0a6dd6a = addy6e92399515cfeb1ca5ccf169a0a6dd6a + '&#117;csd' + '&#46;' + '&#101;d&#117;'; var addy_text6e92399515cfeb1ca5ccf169a0a6dd6a = 'k&#101;dl&#97;y&#97;' + '&#64;' + '&#117;csd' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak6e92399515cfeb1ca5ccf169a0a6dd6a').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy6e92399515cfeb1ca5ccf169a0a6dd6a + '\'>'+addy_text6e92399515cfeb1ca5ccf169a0a6dd6a+'<\/a>';

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).