Extensions of valuations to rational function fields over completions

Author:

Dutta Arpan1ORCID

Affiliation:

1. Department of Mathematics School of Basic Sciences, IIT Bhubaneswar Odisha India

Abstract

AbstractGiven a valued field and its completion , we study the set of all possible extensions of v to . We show that any such extension is closely connected with the underlying subextension . The connections between these extensions are studied via minimal pairs, key polynomials, pseudo‐Cauchy sequences, and implicit constant fields. As a consequence, we obtain strong ramification theoretic properties of . We also give necessary and sufficient conditions for to be dense in .

Publisher

Wiley

Subject

General Mathematics

Reference21 articles.

1. All valuations on k(x)$k(x)$;Alexandru V.;J. Math. Kyoto University,1972

2. A theorem of characterization of residual transcendental extensions of a valuation

3. Minimal pairs of definition of a residual transcendental extension of a valuation

4. Sur une classe de prolongements à k(x)$k(x)$ d'une valuation sur une corp k;Alexandru V.;Rev. Roumaine Math. Pures Appl.,1988

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