Elimination of ramification I: The generalized stability theorem

Kuhlmann, Franz-Viktor

doi:10.1090/S0002-9947-2010-04973-6

Elimination of ramification I: The generalized stability theorem
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by Franz-Viktor Kuhlmann

Trans. Amer. Math. Soc. 362 (2010), 5697-5727

DOI: https://doi.org/10.1090/S0002-9947-2010-04973-6

Published electronically: June 11, 2010

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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 $F|K$ 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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