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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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The supersingular locus of the Shimura variety for $$\hbox {GU}(1, n-1)$$ GU ( 1 , n - 1 ) over a ramified prime
TL;DR: In this paper, the authors considered the problem of describing the basic locus of a Shimura variety in the case of an inert prime and showed that the problem can be solved by the Bruhat-Tits simplicial complex of an algebraic group J over Qp.
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The supersingular locus of the Shimura variety for GU(1,n-1) over a ramified prime
TL;DR: In this article, the authors analyze the geometry of the supersingular locus of the reduction modulo p of a Shimura variety associated to a unitary similitude group GU(1,n-1) over Q, in the case that p is ramified.
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Good and semi-stable reductions of Shimura varieties
TL;DR: In this article, the authors study variants of the local models constructed by the second author and Zhu and consider corresponding integral models of Shimura varieties of abelian type and determine all cases of good, resp. of semi-stable, reduction under tame ramification hypotheses.
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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.
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Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications
TL;DR: In this article, the authors prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety.