TY - UNPB

T1 - The Heisenberg coboundary equation

T2 - appendix to Explicit Chabauty-Kim theory

AU - Dan-Cohen, Ishai

AU - Wewers, Stefan

PY - 2014

Y1 - 2014

N2 - 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analyzed, following an unpublished note by Romyar Sharifi, hereby making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.

AB - 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analyzed, following an unpublished note by Romyar Sharifi, hereby making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.

KW - Mathematics - Number Theory

M3 - ???researchoutput.researchoutputtypes.workingpaper.preprint???

T3 - Arxiv preprint

BT - The Heisenberg coboundary equation

ER -