The p-rank stratification on the Siegel moduli space with Iwahori level structure

Hamacher, Paul

doi:10.1007/s00229-013-0616-z

Cited by 2 publications

(1 citation statement)

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“…For B = Q and a complete lattice chain L, the moduli problem A specializes to the Siegel moduli space A I of principally polarized abelian varieties with Iwahori level structure. In [6], Görtz and Yu compute the dimension of the p-rank 0 locus in A I , and this computation was later generalized in [9] by Hamacher to the case of all p-rank strata. The method is the same in both cases: Determine all KR strata contained in a given p-rank stratum and compute the maximum of their dimensions.…”

Section: Introductionmentioning

confidence: 99%

Kottwitz-Rapoport and p-rank strata in the reduction of Shimura varieties of PEL type

Hartwig¹

2015

Ann. inst. Fourier

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We study the reduction of certain integral models of Shimura varieties of PEL type with Iwahori level structure. On these spaces we have the Kottwitz-Rapoport and the p-rank stratification. We show that the p-rank is constant on a KR stratum, generalizing a result of Ngô and Genestier. We prove an abstract, uniform formula for the p-rank on a KR stratum. In the symplectic and in the unitary case we derive explicit formulas for its value. We apply these formulas to the question of the density of the ordinary locus and to the question of the dimension of the p-rank 0 locus.

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Section: Introductionmentioning

confidence: 99%

Kottwitz-Rapoport and p-rank strata in the reduction of Shimura varieties of PEL type

Hartwig¹

2015

Ann. inst. Fourier

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Compactifications of Subschemes of Integral Models of Shimura Varieties

Lan¹,

Stroh

2018

Forum of Mathematics, Sigma

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We study several kinds of subschemes of mixed characteristic models of Shimura varieties which admit good (partial) toroidal and minimal compactifications, with familiar boundary stratifications and formal local structures, as if they were Shimura varieties in characteristic zero. We also generalize Koecher’s principle and the relative vanishing of subcanonical extensions for coherent sheaves, and Pink’s and Morel’s formulas for étale sheaves, to the context of such subschemes.

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The p-rank stratification on the Siegel moduli space with Iwahori level structure

Cited by 2 publications

References 10 publications

Kottwitz-Rapoport and p-rank strata in the reduction of Shimura varieties of PEL type

Kottwitz-Rapoport and p-rank strata in the reduction of Shimura varieties of PEL type

Compactifications of Subschemes of Integral Models of Shimura Varieties

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