Models of torsors and the fundamental group scheme
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| Autores: | , |
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| Formato: | artículo original |
| Fecha de Publicación: | 2018 |
| Descripción: | Given a relative faithfully at pointed scheme over the spectrum of a discrete valuation ring X !S, this paper is motivated by the study of the natural morphism from the fundamental group scheme of the generic ber X to the generic ber of the fundamental group scheme of X. Given a torsor T !X under an a ne group scheme G over the generic ber of X, we address the question of nding a model of this torsor over X, focusing in particular on the case where G is nite. We provide several answers to this question, showing for instance that, when X is integral and regular of relative dimension 1, such a model exists on some model X0 of X obtained by performing a nite number of N eron blowups along a closed subset of the special ber of X. Furthermore, we show that when G is etale, then we can nd a model of T !X under the action of some smooth group scheme. In the rst part of the paper, we show that the relative fundamental group scheme of X has an interpretation as the Tannaka Galois group of a Tannakian category constructed starting from the universal torsor. |
| País: | Kérwá |
| Institución: | Universidad de Costa Rica |
| Repositorio: | Kérwá |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/85333 |
| Acceso en línea: | https://www.cambridge.org/core/journals/nagoya-mathematical-journal/article/models-of-torsors-and-the-fundamental-group-scheme/6CCB905236E4D15B0EE6136E486914F9 https://hdl.handle.net/10669/85333 |
| Palabra clave: | Torsor Fundamental group scheme Models |