The starting point for this course is Drinfeld's work [Dri80] on the global Langlands
correspondence over function fields. Fix X/Fp a smooth projective curve, with function field K …

Following the idea of [Far16], we develop the foundations of the geometric Langlands
program on the Fargues--Fontaine curve. In particular, we define a category of $\ell $-adic …

We develop a theory of affine flag varieties and of their Schubert varieties for reductive
groups over a Laurent power series local field k ((t)) with ka perfect field. This can be viewed …

This is a survey article that advertizes the idea that there should exist a theory of p-adic local
analogues of Shimura varieties. Prime examples are the towers of rigid-analytic spaces …

We show that the mod $ p $ points on a Shimura variety of abelian type with hyperspecial
level have the form predicted by the conjectures of Kottwitz and Langlands-Rapoport. Along …

We show that, in good residual characteristic, most supercuspidal representations of a
tamely ramified reductive $ p $-adic group $ G $ arise from pairs $(S,\theta) $, where $ S $ is …

A conjecture on Whittaker–Fourier coefficients of cusp forms - ScienceDirect Skip to main
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The tools from Galois cohomology play a fundamental role in modern number theory. They
contribute to a better understanding of the Galois group of a local or a number field, which …

We give the proofs of some simple facts on parahoric subgroups and on Iwahori Weyl
groups used in [T. Haines, The base change fundamental lemma for central elements in …

Abstract We study the Ekedahl–Oort stratification for good reductions of Shimura varieties of
PEL type. These generalize the Ekedahl–Oort strata defined and studied by Oort for the …