We formulate and prove a local arithmetic Siegel–Weil formula for GSpin Rapoport–Zink
spaces, which is a precise identity between the arithmetic intersection numbers of special …

We construct explicit generating series of arithmetic extensions of Kudla's special divisors on
integral models of unitary Shimura varieties over CM fields with arbitrary split levels and …

Abstract The Langlands-Kottwitz method seeks to understand Shimura varieties in terms of
automorphic forms by deriving a trace formula for the cohomology of Shimura varieties …

In this paper we study the geometry of good reductions of Shimura varieties of abelian type.
More precisely, we construct the Newton stratification, Ekedahl-Oort stratification, and central …

These are the notes of a course on Shimura varieties that I gave at the 2022 IHES summer
school on the Langlands program. Lecture 1 gives an introduction to Shimura varieties over …

In this paper we study the geometry of good reductions of Shimura varieties of abelian type.
More precisely, we construct the Newton stratification, Ekedahl-Oort stratification, and central …

A theorem of Grothendieck tells us that if the Galois action on the Tate module of an abelian
variety factors through a smaller field, then the abelian variety, up to isogeny and finite …

Let (G, X) be a Shimura datum of Hodge type, and SK (G, X) its integral model with
hyperspecial (resp. parahoric, assuming the group is unramified) level structure. We prove …