Seminar

Let (R, m) be a local ring of characteristic p with perfect residue field. Let I be an ideal of R. In this talk I will describe some recent results, joint with Ilya Smirnov and Keiichi Watanabe, on the asymptotic behavior of length of the zeroth local cohomology module of R/I^[q]. This is an obvious generalization of the classical concepts of Hilbert-Kunz function and multiplicity.