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

We show that the Hilbert-Kunz multiplicity of a d-dimensional non-regular complete intersection over Fp¯, p>2 prime, is bounded by below by the Hilbert-Kunz multiplicity of ∑i=0dxi2=0, answering positively a conjecture of Watanabe and Yoshida in the case of complete intersections.