TITLE: Detection of valuations using generalized K-theory
ABSTRACT: A main problem
in the birational anabelian geometry is the detection of valuations on
a field F from their
"cohomological footprints" - usually in the mod p cohomology ring H*(F,Z/p). We will first explain
how the new theory of Milnor K-rings
modulo a subgroup of the multiplicative group of F (see [1]) answers this question
in the tame case, and in a sharp way.
We will then consider the most interesting "wild" case, namely, fields F whose maximal pro-p Galois group is a finitely
generated Demushkin group. Finally (and if time allows), we will
discuss some of the remaining open problems in this area.
Reference:
[1] I. Efrat, "Valuations, Orderings, and Milnor K-Theory", American
Mathematical Society, 282 pp., expected publication date: April 2006.
http://www.ams.org/bookstore-getitem/item=surv-124