On the injective dimension of unit Cartier and Frobenius modules

2024/12/11 by Manuel Blickle, Daniel Fink, Blickle, Manuel +4
Mathematics · #13A35 #13D05 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2412.08423

openalex publication_date 2024/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 dim(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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