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Cartier Crystals have finite global dimension
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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.
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Cited by 1 Pith paper
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On the injective dimension of unit Cartier and Frobenius modules
Every unit Cartier module over a noetherian F-finite ring of prime characteristic p has injective dimension at most the dimension of its support plus one; the same holds for unit Frobenius modules over regular rings.
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