Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the cohomological coprimality of Galois representations associated with elliptic curves

Jerome Tomagan Dimabayao

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Let $E$ and $E'$ be elliptic curves over an algebraic number field. We show that systems of $\ell$-adic representations associated with $E$ and $E'$ are cohomologically coprime, in the sense that the Galois cohomology groups corresponding to respective fields of division points are all trivial. This provides a generalization of some known results about the vanishing of the cohomology groups associated with the $\ell$-adic Tate module of an elliptic curve.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 10 (2015), 141-146.

First available in Project Euclid: 2 December 2015

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Zentralblatt MATH identifier

Primary: 11F80: Galois representations 11G05: Elliptic curves over global fields [See also 14H52]

Galois representations elliptic curves


Dimabayao, Jerome Tomagan. On the cohomological coprimality of Galois representations associated with elliptic curves. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 10, 141--146. doi:10.3792/pjaa.91.141.

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