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University of Cambridge > Talks.cam > Number Theory Seminar > The equivariant main conjecture via 1-motives, and applications

## The equivariant main conjecture via 1-motives, and applicationsAdd to your list(s) Download to your calendar using vCal - Cornelius Greither (Munich)
- Tuesday 29 November 2011, 14:30-15:30
- MR13.
If you have a question about this talk, please contact Tom Fisher. This talk presents joint work with
Cristian Popescu. We introduce ``abstract M = M
for every _{S,T}G-Galois extension K/k of global fields (and suitable auxiliary
sets S, T, which are familiar from the theory of L-functions).
Our first main result says that T is cohomologically
trivial over _{l} MG.
We then can show that its Fitting ideal is given by an
equivariant p-adic L-series, very much in the style of other
and earlier Equivariant Main Conjectures.This seems to have many applications; we will discuss two of them.
The first is geometric in nature. We show that the degree zero class number
of the Fermat curve q elements is either 1 or at least divisible
by l. The underlying idea is that cohomological
triviality implies congruences between ^{l-2}L-functions, and these
congruences are arithmetically meaningful. Secondly, we explain
an explicit construction of Tate sequences arising from our
approach. Work in progress indicates that this leads to a proof
of the Rubin-Stark conjecture under certain conditions.This talk is part of the Number Theory Seminar series. ## This talk is included in these lists:- All CMS events
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