**BİLKENT
ALGEBRA – TOPOLOGY SEMINAR**

**"Towards a Refinement of the Bloch – Kato Conjecture"**

By

# CİHAN OKAY

# (University of Western
Ontario)

**Abstract:**
The Bloch-Kato conjecture is the statement that the Galois cohomology of the absolute
Galois group of a field which contains a primitive pth root of unity in mod p coefficients
is isomorphic to Milnor K-theory reduced modulo p. This statement is now a
theorem proved by Rost and Voevodsky. In other words it says that the
cohomology ring of the absolute Galois group is generated by one dimensional
classes. It is a natural question to find intermediate Galois extensions of the
base field where every element in the cohomology ring decomposes into a sum of
products of one dimensional classes. In degree two we answer this question by
providing a tower of Galois extensions where indecomposable elements decompose
in the next level of the tower. We also illustrate this refinement by directly
computing the cohomology rings of superpythagorean fields and p-rigid fields.
This is a joint work with J. Minac and S. Chebolu.

**Date: ****Thursday, August 13, 2015**

**Time: ****13.30-14.30**

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

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**All are most cordially invited.**

Tea and cookies will be served after the talk.