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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('cloak81b6349026746695f644dc848d755bb2').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy81b6349026746695f644dc848d755bb2 = 'k&#101;dl&#97;y&#97;' + '&#64;'; addy81b6349026746695f644dc848d755bb2 = addy81b6349026746695f644dc848d755bb2 + '&#117;csd' + '&#46;' + '&#101;d&#117;'; var addy_text81b6349026746695f644dc848d755bb2 = 'k&#101;dl&#97;y&#97;' + '&#64;' + '&#117;csd' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak81b6349026746695f644dc848d755bb2').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy81b6349026746695f644dc848d755bb2 + '\'>'+addy_text81b6349026746695f644dc848d755bb2+'<\/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).