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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
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The Satake isomorphism for special maximal parahoric Hecke algebras
Thomas J. Haines,Sean Rostami +1 more
TL;DR: In this article, a transfer homomorphism t : HK∗ (G∗) → HK(G) where G∗ is the quasi-split inner form of G is defined.
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Local models of Shimura varieties, I. Geometry and combinatorics
TL;DR: The theory of local models of Shimura varieties has been surveyed in this paper, where the authors give an overview of the results on their geometry and combinatorics obtained in the last 15 years.
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Heights of kudla-rapoport divisors and derivatives of l-functions
TL;DR: In this article, the authors constructed an arithmetic theta lift from harmonic Maass forms of weight 2 n to the arithmetic Chow group of the integral model of a unitary Shimura variety associated with unitary similitude groups of signature (n-1, 1, 1) by associating to a linear combination of Kudla-Rapoport divisors.
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The Geometric Satake Correspondence for Ramified Groups
TL;DR: In this article, the geometrical Satake isomorphism for a reductive group defined over F = k((t)), and split over a tamely ramified extension is proved.
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Complex multiplication cycles and Kudla-Rapoport divisors
TL;DR: In this paper, the intersections of special cycles on a unitary Shimura variety of signature (n-1,1) were studied and it was shown that the intersection multiplicities of these cycles agree with Fourier coefficients of Eisenstein series.
References
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Topological flatness of orthogonal local models in the split, even case. I
TL;DR: In this article, the spin local model is shown to be topologically flat for two minuscule cocharacters mu in root systems of type D. The spin condition was introduced by Pappas and Rapoport and proved in the split, Iwahori case.
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Local models in the ramified case I. The EL-case
Georgios Pappas,Michael Rapoport +1 more
TL;DR: In this article, the flatness conjecture of Rapoport-Zink on local models fails in the presence of ramification and that in that case one has to modify their definition.
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The Satake isomorphism for special maximal parahoric Hecke algebras
Thomas J. Haines,Sean Rostami +1 more
TL;DR: In this article, a Satake isomorphism for the Hecke algebra H of K-bi-invariant compactly supported functions on a nonarchimedean local field was established.