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Elimination of ramification I: The generalized stability theorem


Author: Franz-Viktor Kuhlmann
Journal: Trans. Amer. Math. Soc. 362 (2010), 5697-5727
MSC (2010): Primary 12J10, 13A18; Secondary 12L12, 14B05
DOI: https://doi.org/10.1090/S0002-9947-2010-04973-6
Published electronically: June 11, 2010
MathSciNet review: 2661493
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Abstract: We prove a general version of the ``Stability Theorem'': if $ K$ is a valued field such that the ramification theoretical defect is trivial for all of its finite extensions, and if $ F\vert K$ is a finitely generated (transcendental) extension of valued fields for which equality holds in the Abhyankar inequality, then the defect is also trivial for all finite extensions of $ F$. This theorem is applied to eliminate ramification in such valued function fields. It has applications to local uniformization and to the model theory of valued fields in positive characteristic.


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Additional Information

Franz-Viktor Kuhlmann
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6
Email: fvk@math.usask.ca

DOI: https://doi.org/10.1090/S0002-9947-2010-04973-6
Received by editor(s): May 27, 2008
Published electronically: June 11, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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