On the categorical entropy of the Frobenius pushforward functor

Abstract

In this paper, we consider the Frobenius pushforward endofunctor $F_{\ast }$ of the bounded derived category of finitely generated modules over an $F$-finite noetherian local ring. We completely determine the categorical entropy of $F_{\ast }$ in the sense of Dimitrov, Haiden, Katzarkov, and Kontsevich.

11 pages