Foliations on Shimura varieties in positive characteristic

IF 0.9 1区 数学 Q2 MATHEMATICS
E. Goren, E. D. Shalit
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引用次数: 0

Abstract

This paper is a continuation of a paper by de Shalit and Goren from 2018. We study foliations of two types on Shimura varieties S S in characteristic p p . The first, which we call tautological foliations, are defined on Hilbert modular varieties, and lift to characteristic 0 0 . The second, the V V -foliations, are defined on unitary Shimura varieties in characteristic p p only, and generalize the foliations studied by us before, when the CM field in question was quadratic imaginary. We determine when these foliations are p p -closed, and the locus where they are smooth. Where not smooth, we construct a successive blowup of our Shimura variety to which they extend as smooth foliations. We discuss some integral varieties of the foliations. We relate the quotient of S S by the foliation to a purely inseparable map from a certain component of another Shimura variety of the same type, with parahoric level structure at p p , to S . S.

志村品种正性叶片
本文是de Shalit和Goren 2018年论文的延续。我们在特征p p上研究了下村品种S S上两种类型的叶理。第一个,我们称之为重言叶理,是在希尔伯特模变种上定义的,并提升到特征0。第二个,V-叶理,仅在特征p p p中定义在酉Shimura变种上,并推广了我们以前研究的叶理,当所讨论的CM场是二次虚时。我们确定这些叶理何时是p-p-closed的,以及它们是光滑的轨迹。在不光滑的地方,我们构建了下村品种的连续放大,它们作为光滑的叶理延伸到下村品种。我们讨论了叶理的一些整体变化。我们将S S与叶理的商与一个纯粹不可分割的映射联系起来,该映射来自另一个相同类型的下村品种的某个组成部分,在p p处具有准水平结构,到S。S
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来源期刊
CiteScore
2.70
自引率
5.60%
发文量
23
审稿时长
>12 weeks
期刊介绍: The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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