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arXiv · 2412.08423

On the injective dimension of unit Cartier and Frobenius modules

Manuel Blickle·Daniel Fink·Alexandria Wheeler·Wenliang Zhang
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Abstract

Let $R$ be a regular $F$-finite ring of prime characteristic $p$. We prove that the injective dimension of every unit Frobenius module $M$ in the category of unit Frobenius modules is at most $\operatorname{dim}(\operatorname{Supp}_R(M))+1$. We further show that for unit Cartier modules the same bound holds over any noetherian $F$-finite ring $A$ of prime characteristic $p$. This shows that $\dim A+1$ is a uniform upper bound for the injective dimension of any unit Cartier module over a noetherian $F$-finite ring $A$.

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Manuel Blickle, Daniel Fink, Alexandria Wheeler, Wenliang Zhang. 2024-12-11. On the injective dimension of unit Cartier and Frobenius modules. https://arxiv.org/abs/2412.08423

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