Reduction of Local Uniformization to the rank one case

Details Reduction of Local Uniformization to the rank one case Reduction of Local Uniformization to the rank one case

2012-04-20

arxiv.org/abs/1204.4751v1

Mathematics

Commutative Algebra

22 pages

Scientific paper

The main result of this paper is that in order to prove the local
uniformization theorem for local rings it is enough to prove it for rank one
valuations. Our proof does not depend on the nature of the class of local rings
for which we want to prove local uniformization. We prove also the reductions
for di?erent versions of the local uniformization theorem.

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