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

Florian Enescu; Kazuma Shimomoto

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

Florian Enescu·Kazuma Shimomoto

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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.

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Florian Enescu, Kazuma Shimomoto. 2005-02-14. On the upper semi-continuity of the Hilbert-Kunz multiplicity. https://arxiv.org/abs/math/0502289

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