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December 2015 On the cohomological coprimality of Galois representations associated with elliptic curves
Jerome Tomagan Dimabayao
Proc. Japan Acad. Ser. A Math. Sci. 91(10): 141-146 (December 2015). DOI: 10.3792/pjaa.91.141

Abstract

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.

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Jerome Tomagan Dimabayao. "On the cohomological coprimality of Galois representations associated with elliptic curves." Proc. Japan Acad. Ser. A Math. Sci. 91 (10) 141 - 146, December 2015. https://doi.org/10.3792/pjaa.91.141

Information

Published: December 2015
First available in Project Euclid: 2 December 2015

zbMATH: 06554943
MathSciNet: MR3430202
Digital Object Identifier: 10.3792/pjaa.91.141

Subjects:
Primary: 11F80 , 11G05

Keywords: Elliptic curves , Galois representations

Rights: Copyright © 2015 The Japan Academy

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Vol.91 • No. 10 • December 2015
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