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 .
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