6 papers
Common extensions of valuations to rational function fields
Arpan Dutta, Wael Mahboub
Let (K(X)|K,w) be a valuation transcendental extension of rational function fields and take a minimal pair of definition (a, gamma). In this paper, we characterize those K-conjugat…
A ruled residue theorem for algebraic function fields of curves of prime degree
Arpan Dutta
The Ruled Residue Theorem asserts that given a ruled extension of valued fields, the residue field extension is also ruled. In this paper we analyse the failure of this t…
Tame Key polynomials
Arpan Dutta, Franz-Viktor Kuhlmann
We introduce a new method of constructing complete sequences of key polynomials for simple extensions of tame fields. In our approach the key polynomials are taken to be the minima…
Extensions of valuations to rational function fields over completions
Arpan Dutta
Given a valued field and its completion , we study the set of all possible extensions of to . We show that any such extension is closel…
On the implicit constant fields and key polynomials for valuation algebraic extensions
Arpan Dutta
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 va…
Minimal pairs, inertia degrees, ramification degrees and implicit constant fields
Arpan Dutta
An extension (K(X)|K, v) of valued fields is said to be valuation transcendental if we have equality in the Abhyankar inequality. Minimal pairs of definition are fundamental object…