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arXiv · alg-geom/9612017

Weil classes on abelian varieties

B. J. J. Moonen·Yu. G. Zarhin
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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.

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BibTeXRIS

B. J. J. Moonen, Yu. G. Zarhin. 1996-12-19. Weil classes on abelian varieties. https://arxiv.org/abs/alg-geom/9612017

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