Tate Cycles on Abelian Varieties with Complex Multiplication

Murty, V. Kumar ; Patankar, Vijay M.

Canadian journal of mathematics, Tome 67 (2015) no. 1, pp. 198-213

Résumé

We consider Tate cycles on an Abelian variety $A$ defined over a sufficiently large number field $K$ and having complexmultiplication. We show that there is an effective bound $C\,=\,C(A,\,K)$ so that to check whether a given cohomology class is a Tate class on $A$ , it suffices to check the action of Frobenius elements at primes $v$ of norm $\le \,C$ . We also show that for a set of primes $v$ of $K$ of density 1, the space of Tate cycles on the special fibre ${{A}_{v}}$ of the Néron model of $A$ is isomorphic to the space of Tate cycles on $A$ itself.

Détail

DOI : 10.4153/CJM-2014-001-2

Mots-clés : 11G10, 14K22, abelian varieties, complex multiplication, Tate cycles

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