Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensoring with the Frobenius endomorphism   Let $R$ be a commutative Noetherian Cohen-Macaulay local ring that has
positive dimension and prime characteristic. Li proved that the tensor product
of a finitely generated non-free $R$-module $M$ with the Frobenius endomorphism
${}^{\varphi^n}\!R$ is not maximal Cohen-Macaulay provided that $M$ has rank
and $n\gg 0$. We replace the rank hypothesis with the weaker assumption that
$M$ is locally free on the minimal prime ideals of $R$. As a consequence, we
obtain, if $R$ is a one-dimensional non-regular complete reduced local ring
that has a perfect residue field and prime characteristic, then
${}^{\varphi^n}\!R \otimes_{R}{}^{\varphi^n}\!R$ has torsion for all $n\gg0$.
This property of the Frobenius endomorphism came as a surprise to us since,
over such rings $R$, there exist non-free modules $M$ such that $M\otimes_{R}M$
is torsion-free.

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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas