# Cohomological and numerical dynamical degrees on abelian varieties

## TL;DR

This paper proves that for endomorphisms of abelian varieties over algebraically closed fields, the second cohomological dynamical degree equals the first numerical dynamical degree, establishing a key equality in dynamical degrees.

## Contribution

It establishes the equality of the second cohomological and first numerical dynamical degrees for endomorphisms of abelian varieties in arbitrary characteristic.

## Key findings

- Second cohomological dynamical degree equals first numerical dynamical degree.
- Valid in arbitrary characteristic for abelian varieties.

## Abstract

We show that for an endomorphism of an abelian variety defined over an algebraically closed field of arbitrary characteristic, the second cohomological dynamical degree coincides with the first numerical dynamical degree.