**ODTU-B****I****LKENT ALGEBRAIC GEOMETRY SEM****I****NAR**

**“**Serre's
theorem in group cohomology **”**

by

**ERGUN
YALCIN**

**Abstract:** Let G be a group and let H*(G,Fp) denote the cohomology algebra of G in mod p coefficients. One of the most
important theorems about the algebra structure of H*(G,F2) is Serre's theorem of 1965 where he states that if G is not an
elementary abelian group, then there exists
nontrivial one dimensional classes x1,...,xm in the
first cohomology group such that B(x1)B(x2)...B(xm)=0 in the cohomology algebra
of G.

I will explain some of the consequences of
this theorem in group cohomology and discuss a
variation of it for 2-groups.

All necessary definitions will be given so
the talk will be accessible to a general audience of algebraic geometers.

**References:**

[1] J. P. Serre, Sur la dimension cohomologique
des groups profinis, Topology 3 (1965) 413-420.

[2] J.P. Serre, Une relation dans la cohomologie des p-groups, C.R. Acad. Sci.
Paris 304 (1987) 587-590

** **

**Date:** 23 February, 2007 Friday

**Time:** 15:40

**Place:** Bilkent,
Mathematics Seminar Room SA-141

** **

**Tea and cookies will be served before the
talk.**