相关论文: On the $p$-adic theory of local models

We study the integral models of meta-unitary Shimura varieties through the lens of Scholze's fiber product conjecture. Reformulating Bultel's original construction in terms of moduli stacks of Shtukas and Igusa stacks, we prove the validity…

The special fiber of the local model of a PEL Shimura variety with Iwahori-type level structure admits a cellular decomposition. The set of strata is in a natural way a finite subset of the affine Weyl group determined by the Shimura data.…

Given a Z_p-linear local system over a smooth rigid space, we show that it is crystalline (resp. semi-stable) with respect to any smooth (resp. semi-stable) integral model if and only if its restrictions at many classical points are…

We describe a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of both Berkovich and Huber. We give a thorough development of phi-modules…

For an odd prime p, we construct integral models over p for Shimura varieties with parahoric level structure, attached to Shimura data (G,X) of abelian type, such that G splits over a tamely ramified extension of Q_p. The local structure of…

We prove G\"ortz's combinatorial conjecture \cite{Go01} on dual shellability of admissible sets in Iwahori-Weyl groups, proving that the augmented admissible set $\widehat{\mathrm{Adm}}(\mu)$ is dual shellable for any dominant coweight…

We prove conjectures of Breuil and Breuil-Dembele (C. Breuil, "Sur un probleme de compatibilite local-global modulo p pour GL(2)"), including a generalisation from the principal series to the cuspidal case, subject to a mild global…

Deligne's weight-monodromy conjecture gives control over the poles of local factors of L-functions of varieties at places of bad reduction. His proof in characteristic p was a step in his proof of the generalized Weil conjectures. Scholze…

We compute syntomic cohomology of semistable affinoids in terms of cohomology of $(\varphi,\Gamma)$-modules which, thanks to work of Fontaine-Herr, Andreatta-Iovita, and Kedlaya-Liu, is known to compute Galois cohomology of these affinoids.…

The goal of this paper is to establish Beilinson-Bernstein type localization theorems for quantizations of some conical symplectic resolutions. We prove the full localization theorems for finite and affine type A Nakajima quiver varieties.…

In previous papers we formulated an analogue of the Ichino--Ikeda conjectures for Whittaker--Fourier coefficients of automorphic forms on classical group and the metaplectic group. In the latter case we reduced the conjecture to a local…

We prove the isogeny property for special fibres of integral canonical models of compact Shimura varieties of $A_n$, $B_n$, $C_n$, and $D_n^{\dbR}$ type. The approach used also shows that many crystalline cycles on abelian varieties over…

We study the Euler characteristic of $\ell$-adic local systems on the moduli stack $\mathcal{A}_n$ of principally polarized abelian varieties of dimension $n$ associated to algebraic representations of $\mathbf{GSp}_{2n}$, as virtual…

The aim of this paper is to prove the weight-monodromy conjecture (Deligne's conjecture on the purity of monodromy filtration) for varieties p-adically uniformized by the Drinfeld upper half spaces of any dimension. The ingredients of the…

In this article, we study local models associated to certain Shimura varieties. In particular, we present a resoultion of their singularities. As a consequence, we are able to determine the alternating semisimple trace of the geometric…

We propose a conjectural theory of $p$-integral models of Shimura varieties with level structure at $p$ given by a class of normal subgroups of parahoric subgroups with abelian quotient group. The role of the theory of local models is…

We consider unitary Shimura varieties at places where the totally real field ramifies over $\mbQ$. Our first result constructs comparison isomorphisms between absolute and relative local models in this context, which relies on a…

We study the cohomology of various local Shimura varieties for $GL_n$. This provides an explicit description of the spectral action constructed by Fargues-Scholze in certain cases and allows us to prove some strongly generic part of the…

We show that local-global compatibility (at split primes) away from $p$ holds at all points of the $p$-adic eigenvariety of a definite $n$-variable unitary group. The novelty is we allow non-classical points, possibly non-\'{e}tale over…

We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic $(0,p)$. As a first application we provide a smooth solution (answer) to a conjecture (question) of…