Speaker:
Izabela Vlahu (University of Saskatchewan)
Title:
On henselizations of rational function fields
Abstract:
We consider a valued field (K, v) and an element x which is the limit
of a pseudo Cauchy sequence in K of transcendental type. Now, given a
polynomial f in K[x], we know the degree [K(x):K(f(x))] = deg(f), but
things change drastically when we go to the henselizations of K(x) and
K(f(x)). In the first part of the talk we will give an upper bound for
the degree [K(x)^h :K(f(x))^h]. Then we refine things by taking an
element y in the henselization of K(x), y transcendental over K, and we
ask for the degree [K(x)^h : K(y)^h].