Translator Disclaimer
Open Access
VOL. 43 | 2006 Valuations and local uniformization
Michel Vaquié

Editor(s) Shyuichi Izumiya, Goo Ishikawa, Hiroo Tokunaga, Ichiro Shimada, Takasi Sano

Abstract

We give the principal notions in valuation theory, the value group and the residue field of a valuation, its rank, the compositions of valuations, and we give some classical examples. Then we introduce the Riemann-Zariski variety of a field, with the topology defined by Zariski. In the last part we recall the result of Zariski on local uniformization and give a sketch of the proof in the case of an algebraic surface.

Information

Published: 1 January 2006
First available in Project Euclid: 3 January 2019

MathSciNet: MR2325152

Digital Object Identifier: 10.2969/aspm/04310477

Subjects:
Primary: 12J20 , 13A18 , 14B05 , 14E15 , 14J17

Keywords: local uniformization , resolution of singularities , valuations

Rights: Copyright © 2006 Mathematical Society of Japan

PROCEEDINGS ARTICLE
51 PAGES


SHARE
Back to Top