Bernstein-Sato theory for singular rings in positive characteristic
| Autor: | Jeffries, Jack, Núñez-Betancourt, Luis, Quinlan-Gallego, Eamon |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 |
| Databáze: | arXiv |
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