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The Tate-Oort group scheme TOp

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Reid, Miles (2019) The Tate-Oort group scheme TOp. Proceedings of the Steklov Institute of Mathematics / Trudy Matematicheskogo Instituta imeni V.A. Steklova, 307 . pp. 245-266. doi:10.4213/tm4042

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Official URL: https://doi.org/10.4213/tm4042

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Abstract

Over an algebraically closed field of characteristic p, there are 3 group schemes of order p, namely the ordinary cyclic group Z/p, the multiplicative group μp⊂Gm and the additive group αp⊂Ga. The Tate–Oort group scheme TOp puts these into one happy family, together with the cyclic group of order p in characteristic zero. This paper studies a simplified form of TOp, focusing on its representation theory and basic applications in geometry. A final section describes more substantial applications to varieties having p-torsion in Picτ, notably the 5-torsion Godeaux surfaces and Calabi–Yau 3-folds obtained from TO5-invariant quintics.

Над алгебраически замкнутым полем характеристики p существуют три групповые схемы порядка p, а именно циклическая группа Z/p, мультипликативная группа μp⊂Gm и аддитивная группа αp⊂Ga. Групповая схема Тэйта–Оорта TOp помещает их в единое семейство вместе с циклической группой порядка p в нулевой характеристике. В статье рассматривается упрощённая форма TOp с упором на её теорию представлений и базовые приложения к геометрии. В последнем параграфе описываются более существенные приложения к некоторым многообразиям с p-кручением в Picτ, а именно, к поверхностям Годо с 5-кручением и к трехмерным многообразиям Калаби–Яу, полученным из TO5-инвариантных квинтик.

Item Type: Journal Article
Alternative Title: Групповая схема Тэйта–Оорта TOp
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Calabi-Yau manifolds, Manifolds (Mathematics), Geometry, Algebraic
Journal or Publication Title: Proceedings of the Steklov Institute of Mathematics / Trudy Matematicheskogo Instituta imeni V.A. Steklova
Publisher: Springer
ISSN: 0081-5438
Official Date: 25 November 2019
Dates:
DateEvent
25 November 2019Available
1 July 2019Accepted
Volume: 307
Page Range: pp. 245-266
DOI: 10.4213/tm4042
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: This is a post-peer-review, pre-copyedit version of an article published in Proceedings of the Steklov Institute of Mathematics / Trudy Matematicheskogo Instituta imeni V.A. Steklova. The final authenticated version is available online at: https://doi.org/10.4213/tm4042.
Access rights to Published version: Restricted or Subscription Access
Description:

Co-published as: Trudy Matematicheskogo Instituta imeni V.A.
Steklova, 2019, Vol. 307, pp. 267–290.

RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
1440140National Science Foundationhttp://dx.doi.org/10.13039/501100008982
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