Models of the group schemes of roots of unity
| hal.structure.identifier | Laboratoire de Mathématiques de Versailles [LMV] | |
| dc.contributor.author | MÉZARD, Ariane | |
| hal.structure.identifier | Institut de Mathématiques de Jussieu [IMJ] | |
| dc.contributor.author | ROMAGNY, Matthieu | |
| hal.structure.identifier | Scuola Normale Superiore di Pisa [SNS] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | TOSSICI, Dajano | |
| dc.date.accessioned | 2024-04-04T02:25:24Z | |
| dc.date.available | 2024-04-04T02:25:24Z | |
| dc.date.created | 2011-04-12 | |
| dc.date.issued | 2013 | |
| dc.identifier.issn | 0373-0956 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189883 | |
| dc.description.abstractEn | Let O_K be a discrete valuation ring of mixed characteristics (0,p), with residue field k. Using work of Sekiguchi and Suwa, we construct some finite flat O_K-models of the group scheme \mu_{p^n,K} of p^n-th roots of unity, which we call Kummer group schemes. We set carefully the general framework and algebraic properties of this construction. When k is perfect and O_K is a complete totally ramified extension of the ring of Witt vectors W(k), we provide a parallel study of the Breuil-Kisin modules of finite flat models of \mu_{p^n,K}, in such a way that the construction of Kummer groups and Breuil-Kisin modules can be compared. We compute these objects for n < 4. This leads us to conjecture that all finite flat models of \mu_{p^n,K} are Kummer group schemes. | |
| dc.language.iso | en | |
| dc.publisher | Association des Annales de l'Institut Fourier | |
| dc.title.en | Models of the group schemes of roots of unity | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.5802/aif.2784 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.identifier.arxiv | 1104.2232 | |
| bordeaux.journal | Annales de l'Institut Fourier | |
| bordeaux.page | 1055-1135 | |
| bordeaux.volume | 63 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00672822 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00672822v1 | |
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