Bernstein-Sato polynomials in positive characteristic

Details Bernstein-Sato polynomials in positive characteristic Bernstein-Sato polynomials in positive characteristic

2007-11-23

arxiv.org/abs/0711.3794v3

Mathematics

Algebraic Geometry

26 pages; v.2: new section added, treating the decomposition of an arbitrary D-module under the Euler operators; v.3: final ve

Scientific paper

In characteristic zero, the Bernstein-Sato polynomial of a hypersurface can be described as the minimal polynomial of the action of an Euler operator on a suitable D-module. We consider the analogous D-module in positive characteristic, and use it to define a sequence of Bernstein-Sato polynomials (corresponding to the fact that we need to consider also divided powers Euler operators). We show that the information contained in these polynomials is equivalent to that given by the F-jumping exponents of the hypersurface, in the sense of Hara and Yoshida.

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