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Some elementary theorems about divisibility of 0-cycles on abelian varieties defined over finite fields

Hélène Esnault
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Abstract

If $X$ is an abelian variety over a field and $L$ is an invertible sheaf, we know that the degree of the 0-cycle $L^g$ is divisible by $g!$. As a 0-cycle, it is not, even over a field of cohomological dimension 1. But we show that over a finite field there is perhaps some hope.

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Hélène Esnault. 2003-11-03. Some elementary theorems about divisibility of 0-cycles on abelian varieties defined over finite fields. https://arxiv.org/abs/math/0311023

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