On the Moduli Description of Local Models for Ramified Unitary Groups
TLDR
In this paper, a further refinement to their moduli problem is proposed, which is both necessary and sufficient to characterize the (flat) local model in a certain special maximal parahoric case with signature (n− 1, 1).Abstract:
Local models are schemes which are intended to model the etalelocal structure of p-adic integral models of Shimura varieties. Pappas and Zhu have recently given a general group-theoretic construction of flat local models with parahoric level structure for any tamely ramified group, but it remains an interesting problem to characterize the local models, when possible, in terms of an explicit moduli problem. In the setting of local models for ramified, quasi-split GUn, work towards an explicit moduli description was initiated in the general framework of Rapoport and Zink’s book and was subsequently advanced by Pappas and Pappas–Rapoport. In this paper we propose a further refinement to their moduli problem, which we show is both necessary and sufficient to characterize the (flat) local model in a certain special maximal parahoric case with signature (n− 1, 1).read more
Citations
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Regular formal moduli spaces and arithmetic transfer conjectures
TL;DR: In this article, the authors define various formal moduli spaces of p-divisible groups which are regular, and morphisms between them, and formulate arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture in the presence of ramification.
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On the arithmetic transfer conjecture for exotic smooth formal moduli spaces
TL;DR: In this paper, a local conjecture for arithmetic transfer in the case of an exotic smooth formal moduli space of p-divisible groups, associated to a unitary group relative to a ramified quadratic extension of a p-adic field, was formulated.
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On the arithmetic transfer conjecture for exotic smooth formal moduli spaces
TL;DR: In this article, a local conjecture for arithmetic transfer in the case of an exotic smooth formal moduli space of p-divisible groups, associated to a unitary group relative to a ramified quadratic extension of a p-adic field, was formulated.
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Arithmetic diagonal cycles on unitary Shimura varieties
TL;DR: In this paper, the authors define variants of PEL type of the Shimura varieties that appear in the context of the arithmetic Gan-Gross-Prasad conjecture and formulate for them a version of the AGGP conjecture.
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The supersingular locus of unitary Shimura varieties with exotic good reduction
TL;DR: In this paper, a group-theoretic approach is used to give a concrete description of the geometric structure of the supersingular locus of unitary Shimura varieties with exotic good reduction.
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.
Journal ArticleDOI
Points on some Shimura varieties over finite fields
TL;DR: In this article, the Eichler-Shimura congruence relation was used to make the connection between the Hasse-Weil zeta function and automorphic L-functions.
BookDOI
Period Spaces for p-divisible Groups (AM-141), Volume 141
Michael Rapoport,Thomas Zink +1 more
Journal ArticleDOI
Local models of Shimura varieties and a conjecture of Kottwitz
Georgios Pappas,Xinwen Zhu +1 more
TL;DR: In this paper, a group theoretic definition of local models of Grassmannian degenerations of Shimura varieties has been given, which are obtained by extending constructions of Beilinson, Drinfeld, Gaitsgory and the second-named author to mixed characteristics and to the case of general reductive groups.