Fundamental elements of an affine Weyl group

Nie, Sian

doi:10.1007/s00208-014-1122-7

Cited by 23 publications

(22 citation statements)

References 9 publications

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“…Write , where is a reductive -model of . If is a universal abelian scheme corresponding to some symplectic embedding of , then is naturally a -zip; the classifying map is smooth by Zhang [Zha18] and surjective by Nie [Nie15] and Kisin, Madapusi Pera, and Shin [Kis15].…”

Section: Introductionmentioning

confidence: 99%

Automorphic vector bundles with global sections on -schemes

Goldring¹,

Koskivirta²

2018

Compositio Math.

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A general conjecture is stated on the cone of automorphic vector bundles admitting nonzero global sections on schemes endowed with a smooth, surjective morphism to a stack of G-zips of connected-Hodge-type; such schemes should include all Hodge-type Shimura varieties with hyperspecial level. We prove our conjecture for groups of type A n 1 , C 2 , and Fp-split groups of type A 2 (this includes all Hilbert-Blumenthal varieties and should also apply to Siegel modular threefolds and Picard modular surfaces). An example is given to show that our conjecture can fail for zip data not of connected-Hodge-type.

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Section: Introductionmentioning

confidence: 99%

Automorphic vector bundles with global sections on -schemes

Goldring¹,

Koskivirta²

2018

Compositio Math.

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“…By [38], for m big enough, all level m strata are central leaves. Using the above theorem, as well results in [10], [16], [28], [29] and [40], we can prove the followings. Theorem 2.…”

mentioning

confidence: 63%

“…The goal of this paper is to extend such a theory to good reductions at char p ≥ 3 of Shimura varieties of Hodge type. As a consequence, thanks to results and ideas in [10], [28], [42] and [48], we get a dimension formula for Newton strata.…”

mentioning

confidence: 83%

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Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type

Zhang¹

2018

Can. j. math.

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Abstract. For a Shimura variety of Hodge type with hyperspecial level structure at a prime p, Vasiu and Kisin constructed a smooth integral model (namely the integral canonical model) uniquely determined by a certain extension property. We de ne and study the Ekedahl-Oort strati cations on the special bers of those integral canonical models when p > . is generalizes Ekedahl-Oort strati cations de ned and studied by Oort on moduli spaces of principally polarized abelian varieties and those de ned and studied by Moonen, Wedhorn and Viehmann on good reductions of Shimura varieties of PEL type. We show that the Ekedahl-Oort strata are parameterized by certain elements w in the Weyl group of the reductive group in the Shimura datum. We prove that the stratum corresponding to w is smooth of dimension l(w) (i.e. the length of w) if it is non-empty. We also determine the closure of each stratum.

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“…Recall that a Newton stratum only depends on LG i -σ-conjugacy classes [b i ], and not on individual representatives. A fundamental alcove in [b i ] is an element x bi of W such that all (or one) representative b i,0 in N (L) is contained in [b i ], and such that the length ℓ(x bi ) is minimal with that property, compare [28], Theorem 6.5, or [20]. One can then show that this length is equal to 2ρ G , ν bi where ρ G is the half-sum of the positive roots of G and where ν bi is the dominant We now define formal versions of these subschemes of ∇ µ n H 1 U (C, G).…”

Section: Foliationsmentioning

confidence: 99%