Roy Joshua
The Ohio State University
Title
Algebraic K-theory of Geometric fields and the Carlsson conjecture
Abstract
The main focus of the talk is on the Algebraic K-theory of geometric fields, i.e., fields that contain an algebraically closed subfield. Suslin's theorem from the early 1980s shows that if the bigger field is also algebraically closed, then the algebraic K-theory of the two fields are isomorphic if one works prime to the characteristic.
The Carlsson conjecture is an explicit description of the algebraic K-theory of the bigger field, when it is no longer assumed to be algebraically closed and involves its absolute Galois group in an explicit manner.
The first part of the talk will be a review of Algebraic K-theory, beginning with K_0, then K_1, K_2 Milnor K-theory, and then higher K-theory: this should be accessible to everyone. The second part of the talk will sketch a proof of one major part of the conjecture.
This is joint work with Gunnar Carlsson.