Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free group actions on varieties and the category of modular Galois
  Extensions for finite p-groups   It is known that a finite group G can only act freely on affine n-space if K
has positive characteristic p and G is a p-group. In that case the group action
is "non-linear" and the ring of regular functions must be a trace-surjective
G-algebra. Now let K be an arbitrary field of characteristic p>0 and let G be a
finite p-group. In this paper we study the category Ts of all finitely
generated trace-surjective K-G algebras. In a previous paper we have shown that
the objects in Ts are precisely those finitely generated K-G algebras A such
that the extension of A over the invariant ring A^G is a Galois-extension in
the sense of Chase-Harrison-Rosenberg. Although Ts is not an abelian category
it has "s-projective objects", which are analogues of projective modules, and
it has (s-projective) categorical generators, which we will describe
explicitly. We will show that s-projective objects and their rings of
invariants are retracts of polynomial rings and therefore regular UFDs. The
category Ts also has "weakly initial objects", which are closely related to the
essential dimension of G over K. Our results yield a geometric structure
theorem for free actions of finite p-groups on affine K-varieties. There are
also close connections to open questions on retracts of polynomial rings, to
embedding problems in standard modular Galois-theory of p-groups and,
potentially, to a new constructive approach to homogeneous invariant theory.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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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: acc-phys