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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 (In Press)
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Official URL: https://doi.org/10.4213/tm4042
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 | ||||||
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| 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: |
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| Date of first compliant deposit: | 24 July 2019 | ||||||
| Volume: | 307 | ||||||
| Page Range: | pp. 245-266 | ||||||
| DOI: | 10.4213/tm4042 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | In Press | ||||||
| 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. |
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