Weil classes on abelian varieties
alg-geom
2016-08-30 v1 Algebraic Geometry
Abstract
Consider a complex abelian variety X on which a field F acts. Generalizing a construction of A. Weil, one associates to this a subspace W_F of the cohomology of X, which we call the space of Weil classes w.r.t. F. The purpose of this paper is to answer the following two questions: Q1: under what conditions on F does the space W_F contain, or even consist of, Hodge classes?, Q2: if W_F contains Hodge classes, under what conditions on F are these exceptional? In case X is defined over a number field, we also answer the analogous questions for Tate classes.
Cite
@article{arxiv.alg-geom/9612017,
title = {Weil classes on abelian varieties},
author = {B. J. J. Moonen and Yu. G. Zarhin},
journal= {arXiv preprint arXiv:alg-geom/9612017},
year = {2016}
}
Comments
11 pages, Latex2e