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The test function conjecture for parahoric local models
Thomas J. Haines,Timo Richarz +1 more
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In this article, the authors proved the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure, and their analogues in equal characteristic.Abstract:
We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure, and their analogues in equal characteristic.read more
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Normality and Cohen-Macaulayness of parahoric local models
Thomas J. Haines,Timo Richarz +1 more
TL;DR: In this paper, the singularities of integral models of Shimura varieties and moduli stacks of shtukas with parahoric level structure were studied, and it was shown that the entire local model is normal with reduced special fiber and, if p>2, it is also Cohen-Macaulay.
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Dualities for root systems with automorphisms and applications to non-split groups
TL;DR: For root systems with automorphisms, this article gave a simple uniform description of the Bruhat-Tits echelonnage root system, the Knop root system and the Macdonald root system.
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Białynicki-Birula decomposition for reductive groups
TL;DR: In this paper, the Bialynicki-Birula decomposition is generalized to linear reductive groups on algebraic spaces and finite type schemes, and a relative version of the BB decomposition for algebraic stacks is presented.
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On the normality of Schubert varieties: remaining cases in positive characteristic
Thomas J. Haines,Timo Richarz +1 more
TL;DR: In this paper, the authors studied the geometry of equicharacteristic partial affine flag varieties associated to tamely ramified groups and showed that most Schubert varieties are not normal.
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Spaces with _{}-action, hyperbolic localization and nearby cycles
TL;DR: In this paper, it was shown that hyperbolic localization commutes with nearby cycles and proved Braden's theorem for arbitrary base schemes for any algebraic space with constant action.
References
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Book
Hodge Cycles, Motives, and Shimura Varieties
TL;DR: In this article, Langlands's construction of the Taniyama Group is described, as well as the construction of a Taniya Group for Hodge Cycles on Abelian Varieties.
Book ChapterDOI
Les Schémas de Modules de Courbes Elliptiques
Pierre Deligne,Michael Rapoport +1 more
TL;DR: In this paper, the structure a linfini and the reduction modulo p de X/Γ were studied, where p is the complement of a sous-groupe d'un ensemble fini de points in Riemann compacte.
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.
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Geometric Langlands duality and representations of algebraic groups over commutative rings
Ivan Mirković,Kari Vilonen +1 more
TL;DR: In this article, the basic relationship between G and G is discussed, and a canonical construction of G, starting from G, is presented, which leads to a rather explicit construction of a Hopf algebra by Tannakian formalism.
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Geometric Langlands duality and representations of algebraic groups over commutative rings
Ivan Mirković,Kari Vilonen +1 more