Henkel, Timo (2020)
Classification of BTn-groups over perfectoid rings.
Technische Universität Darmstadt
doi: 10.25534/tuprints-00014223
Ph.D. Thesis, Primary publication, Publisher's Version
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Item Type: | Ph.D. Thesis | ||||
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Type of entry: | Primary publication | ||||
Title: | Classification of BTn-groups over perfectoid rings | ||||
Language: | English | ||||
Referees: | Wedhorn, Prof. Dr. Torsten ; Lau, Prof. Dr. Eike | ||||
Date: | 2020 | ||||
Place of Publication: | Darmstadt | ||||
Collation: | vi, 59 Seiten | ||||
Date of oral examination: | 21 October 2020 | ||||
DOI: | 10.25534/tuprints-00014223 | ||||
Abstract: | In this work, we investigate p-divisible groups over integral perfectoid rings by focussing on the relevant p-power torsion subgroups, which are instances of BTn-groups. We use results of Lau and Anschütz-Le Bras to show that such groups can be described by semi linear algebra objects which live over the tilt of the ground ring. These objects are called BKn-modules. From this classification, we deduce that in our setting every BTn-group can be lifted to a p-divisible group. In the case of local perfectoid rings, we find an explicit description of this data in terms of orbits with respect to a certain group operation. By the connection between BT1-groups and F-Zips, this contains the classification of F-Zips ober a perfect field of characteristic p as a special case. We also deal with globalization aspects of this results. We show that BKn modules can be glued with respect to a certain topology which is fine enough to depict the classifying stack of BKn-modules as a quotient stack. Moreover, we consider our constructions with respect to the finer p-complete arc topology. This topology has a basis consisting of products of perfectoid valuation rings of rank at most 1. Finally, we show globalization results for this topology. In particular, BKn-modules over a perfect ring can be glued together and the resulting stack has a description as a quotient stack. Assuming a conjecture, analogous results are proved for general perfectoid rings. |
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Status: | Publisher's Version | ||||
URN: | urn:nbn:de:tuda-tuprints-142233 | ||||
Classification DDC: | 500 Science and mathematics > 510 Mathematics | ||||
Divisions: | 04 Department of Mathematics > Algebra 04 Department of Mathematics > Algebra > Arithmetic algebraic geometry |
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Date Deposited: | 01 Dec 2020 07:53 | ||||
Last Modified: | 01 Dec 2020 07:53 | ||||
URI: | https://tuprints.ulb.tu-darmstadt.de/id/eprint/14223 | ||||
PPN: | 473154803 | ||||
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