THE TWELFTH COLLOQUIUMFEST

Speaker: Josnei Novacoski (University of Saskatchewan, Canada)

Title: "Reduction of Local Uniformization to the rank one case"

Abstract:
Let R be a local domain dominated by the valuation ring of a
valuation v on K=Quot(R) (in that case we say that v is centered at R).
The problem of Local Uniformization is whether we can find a local ring
R' essentially of finite type over R and dominated by the valuation ring
of v, such that R' is regular. We prove that in order to prove Local
Uniformization for valuations centered at elements of a given category
of local rings, it is enough to prove Local Uniformization for rank one
valuations centered at elements of that category. We present stronger
versions of the Local Uniformization problem and prove the equivalent
results for these stronger versions.