Standard conjectures for abelian fourfolds
Algebraic Geometry
2020-09-03 v3 Number Theory
Abstract
Let A be an abelian fourfold. We prove the Standard Conjecture of Hodge type for A. By combining this result with a theorem of Clozel we deduce that numerical equivalence on A coincides with l-adic homological equivalence on A for infinitely many l. The approach consists in reformulating this question into a p-adic problem and then using p-adic Hodge Theory to solve it.
Cite
@article{arxiv.1806.03216,
title = {Standard conjectures for abelian fourfolds},
author = {Giuseppe Ancona},
journal= {arXiv preprint arXiv:1806.03216},
year = {2020}
}
Comments
Final version, published online in Inventiones Mathematicae. The p-adic part of the paper has been improved following ideas of the referee