The Tate Conjecture for Certain Abelian Varieties over Finite Fields
نویسنده
چکیده
In an earlier work, we showed that if the Hodge conjecture holds for all complex abelian varieties of CM-type, then the Tate conjecture holds for all abelian varieties over finite fields (Milne 1999b). In this article, we extract from the proof a statement (Theorem 1.1) that sometimes allows one to deduce the Tate conjecture for the powers of a single abelian variety A over a finite field from knowing that some Hodge classes on their lifts to characteristic zero are algebraic.
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