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- W2964213648 abstract "Given a relative faithfully flat pointed scheme over the spectrum of a discrete valuation ring $Xrightarrow S$ , this paper is motivated by the study of the natural morphism from the fundamental group scheme of the generic fiber $X_{unicode[STIX]{x1D702}}$ to the generic fiber of the fundamental group scheme of $X$ . Given a torsor $Trightarrow X_{unicode[STIX]{x1D702}}$ under an affine group scheme $G$ over the generic fiber of $X$ , we address the question of finding a model of this torsor over $X$ , focusing in particular on the case where $G$ is finite. 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 $X^{prime }$ of $X_{unicode[STIX]{x1D702}}$ obtained by performing a finite number of Néron blowups along a closed subset of the special fiber of $X$ . Furthermore, we show that when $G$ is étale, then we can find a model of $Trightarrow X_{unicode[STIX]{x1D702}}$ under the action of some smooth group scheme. In the first 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." @default.
- W2964213648 created "2019-07-30" @default.
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- W2964213648 date "2016-12-05" @default.
- W2964213648 modified "2023-10-12" @default.
- W2964213648 title "MODELS OF TORSORS AND THE FUNDAMENTAL GROUP SCHEME" @default.
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- W2964213648 doi "https://doi.org/10.1017/nmj.2016.67" @default.
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