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Pré-Publication, Document De Travail Année : 2010

On the generalised Tate conjecture for products of elliptic curves over finite fields

Bruno Kahn

Résumé

We prove the generalised Tate conjecture for H^3 of products of elliptic curves over finite fields, by slightly modifying an argument of M. Spiess concerning the Tate conjecture. We prove it fully if the elliptic curves run among at most 3 isogeny classes. We also show how things become more intricate from H^4 onwards, for more that 3 isogeny classes.
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Dates et versions

hal-00544321 , version 1 (07-12-2010)
hal-00544321 , version 2 (09-01-2011)

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Bruno Kahn. On the generalised Tate conjecture for products of elliptic curves over finite fields. 2010. ⟨hal-00544321v2⟩
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