Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galois scaffolds and Galois module structure in extensions of
  characteristic $p$ local fields of degree $p^2$   A Galois scaffold, in a Galois extension of local fields with perfect residue
fields, is an adaptation of the normal basis to the valuation of the extension
field, and thus can be applied to answer questions of Galois module structure.
Here we give a sufficient condition for a Galois scaffold to exist in fully
ramified Galois extensions of degree $p^2$ of characteristic $p$ local fields.
This condition becomes necessary when we restrict to $p=3$. For extensions
$L/K$ of degree $p^2$ that satisfy this condition, we determine the Galois
module structure of the ring of integers by finding necessary and sufficient
conditions for the ring of integers of $L$ to be free over its associated order
in $K[Gal(L/K)]$.

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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: econ