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arXiv · 1309.7240

On the vanishing of cohomologies of $p$-adic Galois representations associated with elliptic curves

Jerome T. Dimabayao
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Abstract

Let $K$ be a $p$-adic field and $E$ an elliptic curve over $K$ with potential good reduction. For some large Galois extensions $L$ of $K$ containing all $p$-power roots of unity, we show the vanishing of certain Galois cohomology groups of $L$ with values in the $p$-adic representation associated with $E$. This generalizes some results of Coates, Sujatha and Wintenberger.

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Jerome T. Dimabayao. 2014-09-08. On the vanishing of cohomologies of $p$-adic Galois representations associated with elliptic curves. https://arxiv.org/abs/1309.7240

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