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Tate Cycles on Abelian Varieties with Complex Multiplication

  • V. Kumar Murty (a1) and Vijay M. Patankar (a2)

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 ≤ 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.

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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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