|
| | | | |
| | | |
| Stat |
Members: 3644
Articles: 2'499'343
Articles rated: 2609
16 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Abhyankar places admit local uniformization in any characteristic | | Hagen Knaf
; Franz-Viktor Kuhlmann
; | | Date: |
13 Apr 2003 | | Subject: | Algebraic Geometry; Commutative Algebra MSC-class: 12J10; 14E15 | math.AG math.AC | | Abstract: | We prove that every place $P$ of an algebraic function field $F|K$ of arbitrary characteristic admits local uniformization, provided that the sum of the rational rank of its value group and the transcendence degree of its residue field $FP$ over $K$ is equal to the transcendence degree of $F|K$, and the extension $FP|K$ is separable. We generalize this result to the case where $P$ dominates a regular local Nagata ring $Rsubseteq K$ of Krull dimension $dim Rleq 2$, assuming that the valued field $(K,v_P)$ is defectless, the factor group $v_P F/v_P K$ is torsion-free and the extension of residue fields $FP|KP$ is separable. The results also include a form of monomialization. Further, we show that in both cases, finitely many Abhyankar places admit simultaneous local uniformization on an affine scheme if they have value groups isomorphic over $v_P K$. | | Source: | arXiv, math.AG/0304159 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER