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

2013/09/27 by Jerome T. Dimabayao, Dimabayao, Jerome T.
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1309.7240

22 pages, some mistakes fixed, cohomological coprimality introduced, implications in the global setting added

openalex publication_date 2013/09/27 · arxiv created 2014/09/08 · arxiv updated 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Les représentations ell-adiques associées aux courbes elliptiques sur \Q_p
• Vanishing of some Galois cohomology groups for elliptic curves
• Galois cohomology of elliptic curves over anticyclotomic extensions
• Wild Galois Representations: Elliptic curves over a 3-adic field
• Local Galois Symbols on E x E