On the generalised Tate conjecture for products of elliptic curves over finite fields
Abstract
We prove the generalised Tate conjecture for H3 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 H4 onwards, for more that 3 isogeny classes.
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