12 citations · 34 across the 13 of their papers we have counts for
13 papers
-zips with additional structure on splitting models of Shimura varieties
Xu Shen, Yuqiang Zheng
We construct universal -zips on good reductions of the Pappas-Rapoport splitting models for PEL-type Shimura varieties. We study the induced Ekedahl-Oort stratification, which s…
EKOR strata for Shimura varieties with parahoric level structure
Xu Shen, Chia-Fu Yu, Chao Zhang
In this paper we study the geometry of reduction modulo of the Kisin-Pappas integral models for certain Shimura varieties of abelian type with parahoric level structure. We giv…
Harder-Narasimhan strata and -adic period domains
Xu Shen
We revisit the Harder-Narasimhan stratification on a minuscule -adic flag variety, by the theory of modifications of -bundles on the Fargues-Fontaine curve. We compare the Ha…
On the structure of some p-adic period domains
Miaofen Chen, Laurent Fargues, Xu Shen
We prove the Fargues-Rapoport conjecture for p-adic period domains: for a reductive group G over a p-adic field and a minuscule cocharacter μ of G, the weakly admissible locus coin…
Stratifications in good reductions of Shimura varieties of abelian type
Xu Shen, Chao Zhang
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, an…
On some generalized Rapoport-Zink spaces
Xu Shen
We enlarge the class of Rapoport-Zink spaces of Hodge type by modifying the centers of the associated -adic reductive groups. These such-obtained Rapoport-Zink spaces are called…
Perfectoid Shimura varieties of abelian type
Xu Shen
We prove that Shimura varieties of abelian type with infinite level at are perfectoid. As a corollary, the moduli spaces of polarized K3 surfaces with infinite level at are…
On the cohomology of some simple Shimura varieties with bad reduction
Xu Shen
We determine the Galois representations inside the -adic cohomology of some quaternionic and related unitary Shimura varieties at ramified places. The main results generalize th…
On the -adic cohomology of some -adically uniformized Shimura varieties
Xu Shen
We determine the Galois representations inside the -adic cohomology of some unitary Shimura varieties at split places where they admit uniformization by finite products of Drinf…
-adic families of automorphic forms over some unitary Shimura varieties
Xu Shen
We construct some -dimensional eigenvarieties for finite slope overconvergent eigenforms over some unitary Shimura varieties with signature $(1,n-1)\times(0,n)\times\cdots\times…
On the Hodge-Newton filtration for p-divisible groups with additional structures
Xu Shen
We prove that, for a -divisible group with additional structures over a complete valuation ring of rank one with mixed characteristic , if the Newton polygon and th…
On the Lefschetz trace formula for Lubin-Tate spaces
Xu Shen
We reprove the Lefschetz trace formula for Lubin-Tate spaces, based on the locally finite cell decompositions of these spaces obtained by Fargues, and Mieda's theorem of Lefschetz…
Cell decomposition of some unitary group Rapoport-Zink spaces
Xu Shen
In this paper we study the -adic analytic geometry of the basic unitary group Rapoport-Zink spaces $\M_K$ with signature . Using the theory of Harder-Narasimhan filtrat…