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Local models for ramified unitary groups
TLDR
In this paper, local models associated to certain Shimura varieties are studied and a resoultion of their singularities is presented, which is able to determine the alternating semisimple trace of the geometric Frobenius on the sheaf of nearby cycles.Abstract:
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 Frobenius on the sheaf of nearby cycles.read more
Citations
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Local models, Mustafin varieties and semi-stable resolutions
TL;DR: In this article, the authors analyze singularities of local models and propose a semi-stable resolution of the local models over Schubert varieties of Grassmannian fiber, which is a generalization of the approach suggested by Genestier.
Semi-stable models for some unitary Shimura varieties over ramified primes
TL;DR: In this paper , the authors considered Shimura varieties associated to a unitary group of signature (2 ,n − 2) and gave regular p -adic integral models for these varieties over odd primes p which ramify in the imaginary quadratic field with level subgroup at p given by the stabilizer of a selfdual lattice in the hermitian space.
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Kudla–Rapoport conjecture for Krämer models
TL;DR: In this article , a modified Kudla-Rapoport conjecture for the Krämer model of unitary Rapoport-Zink space at a ramified prime was proposed.
On the geometry of the Pappas-Rapoport models in the (AR) case
TL;DR: In this article , the Pappas-Rapoport splitting model of unitary Shimura varieties of type A for ramified primes is studied and a combinatorial stratification for which the closure relations are computed is introduced.
References
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Book
Period Spaces for p-divisible Groups
Michael Rapoport,Thomas Zink +1 more
TL;DR: In this paper, the relation of "p"-adic period domains to moduli space of arbitrary reductive groups is investigated, and nonarchimedean uniformization theorems for general Shimura varieties are established.
BookDOI
Period Spaces for p-divisible Groups (AM-141), Volume 141
Michael Rapoport,Thomas Zink +1 more
Book
Arithmetic of quadratic forms
TL;DR: In this paper, Kitaoka provides an introduction to quadratic forms that builds from basics up to the most recent results, including lattice theory, Siegel's formula, and some results involving tensor products.