2022/11/21 by Blickle, Manuel, Fink, Daniel · 1 citation
#13D05 13A35 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2211.11466
We show that the category of quasi-coherent Cartier crystals is equivalent to the category of unit Cartier modules on an F-finite noetherian ring R, and that these equivalent categories have finite global dimension, by showing that every quasi-coherent Cartier crystal has a finite injective resolution. The length of the resolution is uniformly bounded by a bound only depending on R. Our result should be viewed as a generalization of a result of Ma showing that the category of unit R[F]-modules over a F-finite regular ring R has finite global dimension dim R + 1.