Compactification minimale et mauvaise réduction

Stroh, Benoît

doi:10.5802/aif.2546

Cited by 7 publications

(6 citation statements)

References 4 publications

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“…On the other hand, it is also desirable to have nice total or partial compactifications of the integral models. For a long time, it was mainly the good reduction integral models or some parahoric variants of them which had been considered at all (see the introductions of [36,78], and [79]). Nevertheless, in recent works by Madapusi Pera (see [50]) and us (with more elementary arguments; see [38,41], and [43], and also [1] and [70]), a general principle has emerged-the difficulties in the construction of compactifications and in the construction of normal integral models with nice local properties are essentially disjoint from each other.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Compactifications of Subschemes of Integral Models of Shimura Varieties

Lan¹,

Stroh

2018

Forum of Mathematics, Sigma

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“…In fact, these integral models with Iwahoric and pro-p-Iwahoric levels at p have been shown to be normal and Cohen-Macaulay. If we use the constructions in this article instead, then we obtain the same (projective normal) minimal compactifications as in [56] and [57], and sufficiently many (but not all) normal and Cohen-Macaulay toroidal compactifications as in [55] and [57], which admit stratifications and formal local descriptions compatible with those in [10] and [30] in characteristic zero. REMARK 16.5.…”

Section: Semiabelian Extensions Of Tautological Objectsmentioning

confidence: 99%

“…REMARK 16.4. The toroidal and minimal compactifications constructed in [55] and [56] are for the Siegel moduli with parahoric levels at p defined by linear algebraic data that are otherwise split, in which case the naive moduli problems as in Example 13.12 are not naive and define good integral models. The constructions rely crucially on the assertion that the integral models (before compactification) are normal, which is shown there using results of [44] and [12].…”

Section: Semiabelian Extensions Of Tautological Objectsmentioning

confidence: 99%

Compactifications of Pel-Type Shimura Varieties in Ramified Characteristics

Lan

2016

Forum of Mathematics, Sigma

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We show that, by taking normalizations over certain auxiliary good reduction integral models, one obtains integral models of toroidal and minimal compactifications of PEL-type Shimura varieties which enjoy many features of the good reduction theory studied as in the earlier works of Faltings and Chai's and the author's. We treat all PEL-type cases uniformly, with no assumption on the level, ramifications, and residue characteristics involved.

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“…We plan to study, in a forthcoming paper in this series, the higherdimensional analogue of X 0 (N ) × X(1) X(M ) (see Stroh [8]).…”

Section: 2mentioning

confidence: 99%