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

被引：5

作者：

Martin, I ^{[1
]}

机构：

[1] Univ Cambridge, Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WA, England

来源：

COMMUNICATIONS IN ALGEBRA | 2022年 / 50卷 / 04期

关键词：

F-signature; F-singularity; divisor; commutative algebra; algebraic geometry;

D O I：

10.1080/00927872.2021.1986057

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1595 / 1605

页数：11

共 16 条

[1] Aberbach IM, 2003, MATH RES LETT, V10, P51
[2] Bruns W., 1993, COHEN MACAULAY RINGS
[3] Carvajal-Rojas, 2017, ARXIV171006887MATHAG
[4] FUNDAMENTAL GROUPS OF F-REGULAR SINGULARITIES VIA F-SIGNATURE
Carvajal-Rojas, Javier
Schwede, Karl
Tucker, Kevin
[J]. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2018, 51 (04): : 993 - 1016
[5] FOSSUM RM, 1973, ERGEBNISSE MATH IHRE, V74
[6] Hartshorne R., 1994, P C ALGEBRAIC GEOMET, V8, P287
[7] Two theorems about maximal Cohen-Macaulay modules
Huneke, C
Leuschke, GJ
[J]. MATHEMATISCHE ANNALEN, 2002, 324 (02) : 391 - 404
[8] DEPTH OF F-SINGULARITIES AND BASE CHANGE OF RELATIVE CANONICAL SHEAVES
Patakfalvi, Zsolt
Schwede, Karl
[J]. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2014, 13 (01) : 43 - 63
[9] Polstra, 2020, ARXIV200204661V2MATH
[10] Se, 2016, ARXIV160300334V1MATH

← 1 2 →