Graus Din\^amicos e Cohomol\'ogicos em Variedades Abelianas

TL;DR

This paper proves a fundamental equality between dynamical and cohomological degrees for endomorphisms of abelian varieties over algebraically closed fields, extending previous results and providing new insights into their dynamical behavior.

Contribution

It establishes the equality of dynamical and cohomological degrees for endomorphisms of abelian varieties over arbitrary characteristic fields, based on recent foundational work.

Findings

Proves $\chi_{2q}(f) = \lambda_q(f)$ for endomorphisms of abelian varieties.

Extends known results to varieties over fields of arbitrary characteristic.

Builds on recent advances by Fei Hu and Truong.

Abstract

We prove that for an endomorphism $f$ of an abelian manifold defined over an algebraically closed field of arbitrary characteristic, $ \chi_ {2q} (f) = \lambda_q (f) $. Note that this paper is based on recent results due to Fei Hu \cite{Hu19}, \cite{Hu-cndd}, \cite{Hu-Tits} e Truong \cite {Truong1611}.