The number of torsion divisors in a strongly F-regular ring is bounded by the reciprocal of F-signature

Abstract

Polstra showed that the cardinality of the torsion subgroup of the divisor class group of a local strongly F-regular ring is finite. We expand upon this result and prove that the reciprocal of the F-signature of a local strongly F-regular ring R bounds the cardinality of the torsion subgroup of the divisor class group of R.