Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ON THE VANISHING OF COHOMOLOGIES OF p-ADIC GALOIS REPRESENTATIONS ASSOCIATED WITH ELLIPTIC CURVES
Jerome T. DIMABAYAO
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2015 Volume 69 Issue 2 Pages 367-386

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Abstract

Let K be a p-adic field and let E be an elliptic curve over K with potential good reduction. For some large Galois extension 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. We use these to prove analogous results in the global case. This generalizes some results of Coates, Sujatha and Wintenberger.

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© 2015 Faculty of Mathematics, Kyushu University
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