Related papers: Mod-$p$ isogeny classes on Shimura varieties with …

Let $F$ be a totally real field in which a prime number $p>2$ is inert. We continue the study of the (generalized) Goren--Oort strata on quaternionic Shimura varieties over finite extensions of $\mathbb F_p$. We prove that, when the…

We construct integral models of Shimura varieties of abelian type with parahoric level structure over odd primes. These models are \'etale locally isomorphic to corresponding local models.

We prove that, for a $p$-divisible group with additional structures over a complete valuation ring of rank one $O_K$ with mixed characteristic $(0,p)$, if the Newton polygon and the Hodge polygon of its special fiber possess a non trivial…

Let $F$ be a real quadratic field in which a fixed prime $p$ is inert, and $E_0$ be an imaginary quadratic field in which $p$ splits; put $E=E_0 F$. Let ${{\rm Sh}}_{1,n-1}$ be the special fiber over $\mathbb{F}_{p^2}$ of the Shimura…

We compute the connected components of arbitrary parahoric level affine Deligne-Lusztig varieties and local Shimura varieties, thus resolving a folklore conjecture in full generality (even for non-quasisplit groups). We achieve this by…

We construct a moduli space $Y^{\mu, \tau}$ of Kisin modules with tame descent datum $\tau$ and with fixed $p$-adic Hodge type $\leq \mu$, for some finite extension $K/\mathbb{Q}_p$. We show that this space is smoothly equivalent to the…

In this article, we prove that a version of Tate conjectures for certain Deligne-Lusztig varieties implies the Kudla-Rapoport conjecture for unitary Shimura varieties with maximal parahoric level at unramified primes. Furthermore, we prove…

Under the assumption that Galois representations associated to Siegel modular forms exist (it is known only for genus at most 2), we show that the cohomology with p-adic integral coefficients of Siegel Varieties, when localized at a…

For a Shimura variety of Hodge type with hyperspecial level structure at a prime $p$, Vasiu and Kisin constructed a smooth integral model (namely the integral canonical model) uniquely determined by a certain extension property. We define…

We show that the mod p cohomology of a smooth projective variety with semistable reduction over K, a finite extension of Qp, embeds into the reduction modulo p of a semistable Galois representation with Hodge-Tate weights in the expected…

We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, and to give a description of these spaces purely in terms of…

We study the \'etale cohomology of Hilbert modular varieties, building on the methods introduced for unitary Shimura varieties in [CS17, CS19]. We obtain the analogous vanishing theorem: in the "generic" case, the cohomology with torsion…

We study the structure of the supersingular locus of the Rapoport--Zink integral model of the Shimura variety for $\mathrm{GU}(2,2)$ over a ramified odd prime with the special maximal parahoric level. We prove that the supersingular locus…

Let $\mathfrak F$ be a locally compact nonarchimedean field with residue characteristic $p$ and $G$ the group of $\mathfrak{F}$-rational points of a connected split reductive group over $\mathfrak{F}$. We define a torsion pair in the…

Consider a Shimura variety of Hodge type admitting a smooth integral model S at an odd prime p>3. Consider its perfectoid cover S(p^\infty) and the Hodge-Tate period map introduced by A. Caraiani and P. Scholze. We compare the pull-back to…

We study $p$-adic properties of the coherent cohomology of some automorphic sheaves on the Hilbert modular variety $X$ for a totally real field $F$ in the case where the prime $p$ is totally split in $F$. More precisely, we develop higher…

We study the set of connected components of certain unions of affine Deligne-Lusztig varieties arising from the study of Shimura varieties. We determine the set of connected components for basic $\s$-conjugacy classes. As an application, we…

We construct canonical non-vanishing global sections of powers of the Hodge bundle on each Ekedahl-Oort stratum of a Hodge type Shimura variety. In particular we recover the quasi-affineness of the Ekedahl-Oort strata. In the projective…

We develop a theory of $p$-adic automorphic forms on unitary groups that allows $p$-adic interpolation in families and holds for all primes $p$ that do not ramify in the reflex field $E$ of the associated unitary Shimura variety. If the…

We study the singularities of integral models of Shimura varieties and moduli stacks of shtukas with parahoric level structure. More generally our results apply to the Pappas-Zhu and Levin mixed characteristic parahoric local models, and to…