1. Bernstein-Sato theory for singular rings in positive characteristic
- Author
-
Jeffries, Jack, Núñez-Betancourt, Luis, and Quinlan-Gallego, Eamon
- Subjects
Mathematics - Algebraic Geometry ,Mathematics::Commutative Algebra ,Applied Mathematics ,General Mathematics ,FOS: Mathematics ,Mathematics - Commutative Algebra ,Commutative Algebra (math.AC) ,Algebraic Geometry (math.AG) - Abstract
The Bernstein-Sato polynomial is an important invariant of an element or an ideal in a polynomial ring or power series ring of characteristic zero, with interesting connections to various algebraic and topological aspects of the singularities of the vanishing locus. Work of Musta\c{t}\u{a}, later extended by Bitoun and the third author, provides an analogous Bernstein-Sato theory for regular rings of positive characteristic. In this paper, we extend this theory to singular ambient rings in positive characteristic. We establish finiteness and rationality results for Bernstein-Sato roots for large classes of singular rings, and relate these roots to other classes of numerical invariants defined via the Frobenius map. We also obtain a number of new results and simplified arguments in the regular case., Comment: v2: minor fixes after referee report; 58 pages; comments appreciated
- Published
- 2023