Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The action of the Frobenius map on rank 2 vector bundles over genus 2
  curves in small characteristics   Let $X$ be genus 2 curve defined over an algebraically closed field of
characteristic $p$ and let $X\_1$ be its $p$-twist. Let $M\_X$ (resp.
$M\_{X\_1}$) be the (coarse) moduli space of semi-stable rank 2 vector bundles
with trivial determinant over $X$ (resp. $X\_1$). The moduli space $M\_X$ is
isomorphic to the 3-dimensional projective space and is endowed with an action
of the group $J[2]$ of order 2 line bundles over $X$. When $3\leq p \leq 7$, we
show that the Verschiebung (i.e., the separable part of the action of Frobenius
by pull-back) $V : M\_{X\_1} \dashrightarrow M\_X$ is completely determined by
its restrictions to the lines that are invariant under the action of a non zero
element of $J[2]$. Those lines correspond to elliptic curves that appear as
Prym varieties and the Verschiebung restricts to the morphism induced by
multiplication by $p$. Therefore, we are able to compute the explicit equations
of the Verschiebung when the base field has characteristic 3, 5 or 7.

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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom