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

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

2005-02-14

arxiv.org/abs/math/0502289v1

Mathematics

Commutative Algebra

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

Scientific paper

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.

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