Vanishing of Some Galois Cohomology Groups for Elliptic Curves

  title={Vanishing of Some Galois Cohomology Groups for Elliptic Curves},
  author={T. Lawson and C. Wuthrich},
  • T. Lawson, C. Wuthrich
  • Published 2015
  • Mathematics
  • Let \(E/\mathbb {Q}\) be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of \(\mathbb {Q}\) obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group \(H^1\bigl ( G, E[p]\bigr )\) does not vanish, and investigate the analogous question for \(E[p^i]\) when \(i>1\). We include an application to the verification of certain cases of the Birch and Swinnerton-Dyer conjecture, and another… CONTINUE READING
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    Vanishing of Some Cohomology Groups and Bounds for the Shafarevich-Tate Groups of Elliptic Curves
    • 13
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    The image of Galois representations attached to elliptic curves with an isogeny
    • 7
    • PDF
    On elliptic curves with an isogeny of degree 7
    • 9
    • PDF
    On the local-global principle for divisibility in the cohomology of elliptic curves
    • 10
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    • PDF
    Explicit isogeny descent on elliptic curves
    • 12
    • PDF
    Algorithms for Modular Elliptic Curves
    • 776
    Cohomology of number fields
    • 625