BİLKENT
ALGEBRAIC TOPOLOGY SEMINAR

"Galois
Cohomology, Spectral Sequences, and Local Class Field Theory"

By

Matteo Paganin

(Sabanci University)

Abstract: In the first part of this talk, I will sketch the ideas and definitions
of Cohomology for Profinite
Groups. The main example will be the absolute Galois group of a field K. In the
second part, I will introduce an extension of the Hochschild-Serre
Spectral Sequence for a profinite group G and an open
normal subgroup H that also takes into  account the Tate Cohomology of the group G/H. Under certain conditions, this
spectral sequence converges to zero. In particular situations, this fact
implies the existence of families of isomorphisms and
long exact sequences. In the case of a finite Galois extension of local fields,
the results obtained provide a new interpretation of the Reciprocity Map of
Local Class Field Theory.

Date:
Monday, March 19, 2012

Time: 13.40-14.30

Place: Mathematics Seminar Room,
SA-141

Tea
and cookies will be served after the talk.