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math.AG2023
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…
math.AG2022
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…
math.AG2021
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…
math.AG2021
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…