Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Frobenius Complexity of a Local Ring of Prime Characteristic   We introduce a new invariant for local rings of prime characteristic, called
Frobenius complexity, that measures the abundance of Frobenius actions on the
injective hull of the residue field of a local ring. We present an important
case where the Frobenius complexity is finite, and prove that complete, normal
rings of dimension two or less have Frobenius complexity less than or equal to
zero. Moreover, we compute the Frobenius complexity for the determinantal ring
obtained by modding out the $2 \times 2$ minors of a $2 \times 3$ matrix of
indeterminates, showing that this number can be positive, irrational and
depends upon the characteristic. We also settle a conjecture of Katzman,
Schwede, Singh and Zhang on the infinite generation of the ring of Frobenius
operators of a local normal complete $\mathbb{Q}$-Gorenstein ring.

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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th