Texas A&M University, Department of
Mathematics, 216 Milner Hall, 3rd of December 2003, 3:00-4:00
Groups and Dynamcs Seminar
Reducing the
Fontaine-Mazur conjecture to group theory
Nigel Boston of
University of Wisconsin at Madison
The Fontaine-Mazur conjecture characterizes which p-adic Galois
representations should come from algebraic geometry and has had
profound influence. The Galois groups of infinite p-extensions
unramified at p are a mystery, but the F-M conjecture implies they are
not p-adic analytic (in fact they should be related to branch groups).
In this talk, I demystify these Galois groups and give a two-step
approach (both purely group theory) for verifying F-M in these cases.
The first step seeks to characterize those pro-p groups satisfying
conditions coming out of the number theory, while the second step seeks
to show these groups have no infinite p-adic analytic quotients. I
shall illustrate this approach in some specific cases.