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arXiv · 1811.11022

Global Frobenius Betti numbers and F-splitting ratio

Alessandro De Stefani·Thomas Polstra·Yongwei Yao
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Abstract

We extend the notion of Frobenius Betti numbers and F-splitting ratio to large classes of finitely generated modules over rings of prime characteristic, which are not assumed to be local. We also prove that the strong F-regularity of a pair $(R,\mathscr{D})$, where $\mathscr{D}$ is a Cartier algebra, is equivalent to the positivity of the global F-signature ${\rm s}(R,\mathscr{D})$ of the pair. This extends a result previously proved by these authors, by removing an extra assumption on the Cartier algebra.

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Alessandro De Stefani, Thomas Polstra, Yongwei Yao. 2018-11-27. Global Frobenius Betti numbers and F-splitting ratio. https://arxiv.org/abs/1811.11022

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