| Description |
Polstra showed that the cardinality of the torsion subgroup of the divisor class group of a local strongly F-regular ring is finite. In this thesis, we first provide an expository introduction to the field of F-singularities before improving upon Polstra's result by proving 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. Sections 2, 3, and 4 are intended to provide background on relevant theory, section 5 presents new proofs of known results and slight modifications of generally known results, section 6 contains the main contributions of this thesis, and section 7 describes efforts to generalize both our primary result and more broadly the main theorems pertaining to F-singularities. |
