On the categorical entropy of the Frobenius pushforward functor

TL;DR

This paper calculates the categorical entropy of the Frobenius pushforward functor on derived categories over certain rings, providing a complete characterization in this mathematical setting.

Contribution

It provides a complete determination of the categorical entropy of the Frobenius pushforward functor on derived categories over F-finite noetherian local rings.

Findings

Categorical entropy of $F_*$ is explicitly determined.

Results apply to derived categories over F-finite noetherian local rings.

Advances understanding of functor dynamics in algebraic geometry.

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.