[Turkmath:630] Bilkent Algebra-Topology Seminar

[Ergun Yalcin]

Ilgilenen herkesi bekleriz.

Ergun Yalcin



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BILKENT ALGEBRA-TOPOLOGY SEMINAR

Speaker: Cihan Okay (University of Western Ontario, Canada)

Time: Aug 13, Thursday, 13:30-14:30

Place: Bilkent Math Department Seminar Room

Title: Towards a refinement of the Bloch-Kato conjecture

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.

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