The Heisenberg coboundary equation: appendix to Explicit Chabauty-Kim theory

Ishai Dan-Cohen, Stefan Wewers

Research output: Working paper/PreprintPreprint

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Abstract

Let p be a regular prime number, let Gp denote the Galois group of the maximal unramified away from p extension of Q, and let H_et denote the Heisenberg group over Qp with Gp-action given by H_et = Qp(1)^2 \oplus Qp(2). Although Soulé vanishing guarantees that the map H^1(Gp, H_et) ---> H^1(Gp, Qp(1)^2) is bijective, the problem of constructing an explicit lifting of an arbitrary cocycle in H^1(Gp, Qp(1)^2) proves to be a challenge. We explain how we believe this problem should be analyzed, following an unpublished note by Romyar Sharifi, hereby making the original appendix to Explicit Chabauty-Kim theory available online in an arXiv-only note.
Original languageEnglish
StatePublished - 2014

Publication series

NameArxiv preprint

Keywords

  • Mathematics - Number Theory

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