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

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

2011-01-10

arxiv.org/abs/1101.1730v1

Mathematics

Algebraic Geometry

Scientific paper

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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