Cartier Crystals have finite global dimension
- Resource Type
- Working Paper
- Authors
- Blickle, Manuel; Fink, Daniel
- Source
- Subject
- Mathematics - Commutative Algebra
13D05 13A35
- Language
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.
Comment: 11 pages