On the upper semi-continuity of the Hilbert-Kunz multiplicity

Abstract

We show that the Hilbert-Kunz multiplicity of a $d$-dimensional nonregular complete intersection over the algebraic closure of $F_p$, $p>2$ prime, is bounded by below by the Hilbert-Kunz multiplicity of the hypersurface ${\sum }_{i=0}^d{x}_i^2=0$, answering positively a conjecture of Watanabe and Yoshida in the case of complete intersections.

14 pages, preprint version, final version to appear in Journal of Algebra, 285, no 1, 222-237