On generalized Hilbert-Kunz function and multiplicity

Hailong Dao, Ilya Smirnov

Let $(R,\mathfrak{m})$ be a local ring of characteristic $p>0$ and $M$ a finitely generated $R$-module. In this note we consider the limit: $\lim_{n\to \infty} \frac{\ell(H^0_{\math…