Henkel, Timo (2020)
Classification of BTn-groups over perfectoid rings.
Technische Universität Darmstadt
doi: 10.25534/tuprints-00014223
Dissertation, Erstveröffentlichung, Verlagsversion
Kurzbeschreibung (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.
Typ des Eintrags: | Dissertation | ||||
---|---|---|---|---|---|
Erschienen: | 2020 | ||||
Autor(en): | Henkel, Timo | ||||
Art des Eintrags: | Erstveröffentlichung | ||||
Titel: | Classification of BTn-groups over perfectoid rings | ||||
Sprache: | Englisch | ||||
Referenten: | Wedhorn, Prof. Dr. Torsten ; Lau, Prof. Dr. Eike | ||||
Publikationsjahr: | 2020 | ||||
Ort: | Darmstadt | ||||
Kollation: | vi, 59 Seiten | ||||
Datum der mündlichen Prüfung: | 21 Oktober 2020 | ||||
DOI: | 10.25534/tuprints-00014223 | ||||
URL / URN: | https://tuprints.ulb.tu-darmstadt.de/14223 | ||||
Kurzbeschreibung (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. |
||||
Alternatives oder übersetztes Abstract: |
|
||||
Status: | Verlagsversion | ||||
URN: | urn:nbn:de:tuda-tuprints-142233 | ||||
Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik | ||||
Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Algebra 04 Fachbereich Mathematik > Algebra > Arithmetische algebraische Geometrie |
||||
Hinterlegungsdatum: | 01 Dez 2020 07:53 | ||||
Letzte Änderung: | 08 Dez 2020 10:26 | ||||
PPN: | |||||
Referenten: | Wedhorn, Prof. Dr. Torsten ; Lau, Prof. Dr. Eike | ||||
Datum der mündlichen Prüfung / Verteidigung / mdl. Prüfung: | 21 Oktober 2020 | ||||
Export: | |||||
Suche nach Titel in: | TUfind oder in Google |
Frage zum Eintrag |
Optionen (nur für Redakteure)
Redaktionelle Details anzeigen |