Rational Tate classes
Algebraic Geometry
2021-01-19 v3 Number Theory
Abstract
In despair, as Deligne (2000) put it, of proving the Hodge and Tate conjectures, we can try to find substitutes. For abelian varieties in characteristic zero, Deligne (1982) constructed a theory of Hodge classes having many of the properties that the algebraic classes would have if the Hodge conjecture were known. In this article I investigate whether there exists a theory of "rational Tate classes" on varieties over finite fields having the properties that the algebraic classes would have if the Hodge and Tate conjectures were known. v3. Submitted version.
Keywords
Cite
@article{arxiv.0707.3167,
title = {Rational Tate classes},
author = {J. S. Milne},
journal= {arXiv preprint arXiv:0707.3167},
year = {2021}
}