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Presented By: Group, Lie and Number Theory Seminar - Department of Mathematics

GLNT: The p-adic cohomology of the Drinfeld and Lubin-Tate towers

Gabriel Dospinescu, École normale supérieure de Lyon

In this series of talks I will try to give an overview of the main issues that arise when trying to establish mod p and p-adic analogues of the theorems of Langlands, Deligne, Drinfeld and Carayol, describing the l-adic (l ≠ p) étale cohomology of the Drinfeld and Lubin-Tate towers. The methods are very different, based on perfectoid spaces, representation theory of GL2(Qp) and its inner form, as well as syntomic cohomology and the six-functor formalism due to Lucas Mann. This is based on joint work with Colmez and Niziol (for the Drinfeld tower) and Camargo (for the Lubin-Tate tower).

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