Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Models of torsors and the fundamental group scheme   Given a relative faithfully flat pointed scheme over the spectrum of a
discrete valuation ring $X \to S$ this paper is motivated by the study of the
natural morphism from the fundamental group scheme of the generic fiber $X_\eta
$ to the generic fiber of the fundamental group scheme of $X$. Given a torsor
$T \to X_\eta $ under an affine group scheme $G$ over the generic fiber of $X$,
we address the question to find a model of this torsor over $X$, focusing in
particular on the case where $G$ is finite. We obtain partial 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 of $X_{\eta}$
obtained by performing a finite number of N\'eron blow-ups along a closed
subset of the special fiber of $X$. In the first part 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.

3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc