THE THIRTEENTH COLLOQUIUMFEST

Speaker: 
Anna Blaszczok (University of Silesia)

Title: 
Towers of Artin-Schreier defect extensions of rational function fields

Abstract: 
In connection with problems of algebraic geometry like local uniformization,
we consider defect extensions of rational function fields
in two variables over fields of positive characteristic. Since the towers
of Artin-Schreier defect extensions play a central role in the issue of
defect extensions, we study the problem of constructing infinite towers
of such extensions.

We classify Artin-Schreier defect extensions into "dependent" and
"independent" ones, according to whether they are connected with
purely inseparable defect extensions or not. We consider various valuations
of the rational function field and investigate for which it admits
infinite towers of dependent or independent Artin-Schreier defect extensions.
We give also a criterion for a valued field of positive characteristic
p with p-divisible value group and perfect residue field to admit an
infnite tower of dependent Artin-Schreier defect extensions.