Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torsors over the Rational Double Points in Characteristic $\mathbf{p}$   We study torsors under finite group schemes over the punctured spectrum of a
singularity $x\in X$ in positive characteristic. We show that the Dieudonn\'e
module of the (loc,loc)-part
$\mathrm{Picloc}^{\mathrm{loc},\mathrm{loc}}_{X/k}$ of the local Picard sheaf
can be described in terms of local Witt vector cohomology, making
$\mathrm{Picloc}^{\mathrm{loc},\mathrm{loc}}_{X/k}$ computable. Together with
the class group and the abelianised local \'etale fundamental group,
$\mathrm{Picloc}^{\mathrm{loc},\mathrm{loc}}_{X/k}$ completely describes the
finite abelian torsors over $X\setminus\{x\}$. We compute
$\mathrm{Picloc}^{\mathrm{loc},\mathrm{loc}}_{X/k}$ for every rational double
point singularity, which complements results of Artin and Lipman, who
determined ${\pi_{\mathrm{loc}}^{\mathrm{et}}}(X)$ and ${\rm Cl}(X)$. All three
objects turn out to be finite. We extend the Flenner--Mumford criterion for
smoothness of a normal surface germ $x \in X$ to perfect fields of positive
characteristic, generalising work of Esnault and Viehweg: If $k$ is
algebraically closed, then $X$ is smooth if and only if
$\mathrm{Picloc}^{\mathrm{loc},\mathrm{loc}}_{X/k}$,
${\pi_{\mathrm{loc}}^{\mathrm{et}}}(X)$, and ${\rm Cl}(X)$ are trivial.
Finally, we study the question whether rational double point singularities are
quotient singularities by group schemes and if so, whether the group scheme is
uniquely determined by the singularity. We give complete answers to both
questions, except for some $D_n^r$-singularities in characteristic $2$. In
particular, we will give examples of (F-injective) rational double points that
are not quotient singularities.

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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph