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 $R$.

9 pages. Communications in Algebra (2021)

References in corpus (1)

• Two theorems about maximal Cohen--Macaulay modules

Cited by in corpus (3)

• The F-signature Function on the Ample Cone
• Tame fundamental groups of pure pairs and Abhyankar's lemma
• Singularities of determinantal pure pairs