English

A transformation rule for natural multiplicities

Commutative Algebra 2020-02-27 v3 Algebraic Geometry

Abstract

For multiplicities arising from a family of ideals we provide a general approach to transformation rules for a ring extension \'etale in codimension one. Our result can be applied to bound the size of the local \'etale fundamental group of a singularity in terms of F-signature, recovering a recent result of Carvajal-Rojas, Schwede, and Tucker, and differential signature, providing the first characteristic-free effective bound.

Keywords

Cite

@article{arxiv.1904.07755,
  title  = {A transformation rule for natural multiplicities},
  author = {Jack Jeffries and Ilya Smirnov},
  journal= {arXiv preprint arXiv:1904.07755},
  year   = {2020}
}

Comments

12 pages, comments are welcome

R2 v1 2026-06-23T08:41:33.462Z