We formulate a few conjectures on some hypothetical coherent sheaves on the stacks of
arithmetic local Langlands parameters, including their roles played in the local-global …

In this article, we study the Beilinson–Bloch–Kato conjecture for motives associated to
Rankin–Selberg products of conjugate self-dual automorphic representations, within the …

We prove that the generic part of the mod l cohomology of Shimura varieties associated to
quasi-split unitary groups of even dimension is concentrated above the middle degree …

Abstract Let (G, X)(G, X) be a Shimura datum of Hodge type. Let p be an odd prime such that
G _ Q _p GQ p splits after a tamely ramified extension and p\not ∣| π _1 (G^ der)| p∤| π 1 (G …

Using the work of Fargues-Scholze, we prove a vanishing theorem for the generic
unramified part of the cohomology of local Shimura varieties of general linear groups. This …

We study the étale cohomology of Hilbert modular varieties, building on the methods
introduced by Caraiani and Scholze for unitary Shimura varieties. We obtain the analogous …

We study several kinds of subschemes of mixed characteristic models of Shimura varieties
which admit good (partial) toroidal and minimal compactifications, with familiar boundary …

We construct functorial Igusa stacks for all Hodge-type Shimura varieties, proving a
conjecture of Scholze and extending earlier results of the fourth-named author for PEL-type …

R.–On montre que l'action galoisienne sur la partie sans multiplication complexe de
la cohomologie étale d'un faisceau-adique lisse automorphe sur une variété de Shimura …

In this introductory article, we will explain what Shimura varieties are and why they are
useful, with an emphasis on examples. We will also describe various compactifications of …