F-thresholds and Bernstein-Sato polynomials

Mircea Mustata, Shunsuke Takagi, Kei-ichi Watanabe

Published 2004-11-08Version 1

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.