Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaffolds and integral Hopf Galois module structure on purely
  inseparable extensions   Let $p$ be prime. Let $L/K$ be a finite, totally ramified, purely inseparable
extension of local fields, $\left[ L:K\right] =p^{n},\;n\geq2.$ It is known
that $L/K$ is Hopf Galois for numerous Hopf algebras $H,$ each of which can act
on the extension in numerous ways. For a certain collection of such $H$ we
construct "Hopf Galois scaffolds" which allow us to obtain a Hopf analogue to
the Normal Basis Theorem for $L/K.$ The existence of a scaffold structure
depends on the chosen action of $H$ on $L.$ We apply the theory of scaffolds to
describe when the fractional ideals of $L$ are free over their associated
orders in $H.$

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The categories of this paper are: cs
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph