F-thresholds and Bernstein-Sato polynomials

Details F-thresholds and Bernstein-Sato polynomials F-thresholds and Bernstein-Sato polynomials

2004-11-08

arxiv.org/abs/math/0411170v1

European Congress of Mathematics, 341--364, Eur. Math. Soc., Z\"urich, 2005.

Mathematics

Algebraic Geometry

22 pages, submitted to the Proceedings of the 4th ECM, Stockolm, 2004

Scientific paper

We introduce and study invariants of singularities in positive characteristic called F-thresholds. They give an analogue of the jumping coefficients of multiplier ideals in characteristic zero. We discuss the connection between the invariants of an ideal in characteristic zero and the invariants of the different reduction mod p of this ideal. Our main point is that this relation depends on arithmetic properties of p. We also describe a new connection between invariants mod p and the roots of the Bernstein-Sato polynomial.

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