Rational Tate classes

zbMATH Open1181.14010arXiv0707.3167MaRDI QIDQ3649460

J. S. Milne

Publication date: 4 December 2009

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.

Full work available at URL: https://arxiv.org/abs/0707.3167

zbMATH Keywords

finite fieldsabelian varietiesTate conjecture

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Arithmetic ground fields for abelian varieties (14K15) Algebraic cycles (14C25)

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