On the implicit constant fields and key polynomials for valuation algebraic extensions
Algebraic Geometry
2021-11-30 v1 Commutative Algebra
Abstract
This article is a natural construction of our previous works. In this article, we employ similar ideas due to MacLane to provide an estimate of IC(K(X)|K,v) when (K(X)|K,v) is a valuation algebraic extension. Our central result is an analogue of the estimate obtained in the valuation transcendental case. We further provide a natural construction of a complete sequence of key polynomials for v over K in the setting of valuation algebraic extensions.
Keywords
Cite
@article{arxiv.2111.14344,
title = {On the implicit constant fields and key polynomials for valuation algebraic extensions},
author = {Arpan Dutta},
journal= {arXiv preprint arXiv:2111.14344},
year = {2021}
}