Cohomological and numerical dynamical degrees on abelian varieties

Hu, Fei

doi:10.2140/ant.2019.13.1941

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Cohomological and numerical dynamical degrees on abelian varieties

Fei Hu

Vol. 13 (2019), No. 8, 1941–1958

DOI: 10.2140/ant.2019.13.1941

Abstract

We show that for a self-morphism 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.

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Keywords

dynamical degree, abelian variety, endomorphism algebra, étale cohomology, algebraic cycle, positive characteristic

Mathematical Subject Classification 2010

Primary: 14G17

Secondary: 14K05, 16K20

Milestones

Received: 23 October 2018

Revised: 17 April 2019

Accepted: 15 July 2019

Published: 9 October 2019

Authors

Fei Hu
Department of Mathematics University of British Columbia Vancouver BC Canada

Vol. 13, No. 8, 2019