Arpan Dutta

activity

20192021

collaborators

5 papers

math.AG2021

On the ranks and implicit constant fields of valuations induced by pseudo monotone sequences

Arpan Dutta

Given a valued field $(K, v)$ and a pseudo monotone sequence $E$ in $(K, v)$ , one has an induced valuation $v_{E}$ extending $v$ to $K (X)$ . After fixing an extension of $v_{E}$ to a fixe…

math.AG2021

Minimal pairs, minimal fields and implicit constant fields

Arpan Dutta

Minimal pairs of definition were introduced by Alexandru, Popescu and Zaharescu to study residue transcendental extensions. In this paper we obtain analogous results in the value t…

math.AC2020

On the non-uniqueness of maximal purely wild extensions

Arpan Dutta

In this paper we illustrate certain criteria which are sufficient for a henselian valued field to admit non-isomorphic maximal purely wild extensions.

math.AC2019

Eliminating Tame Ramification: generalizations of Abhyankar's Lemma

Franz-Viktor Kuhlmann, Arpan Dutta

A basic version of Abhyankar's Lemma states that for two finite extensions $L$ and $F$ of a local field $K$ , if $L ∣ K$ is tamely ramified and if the ramification index of $L ∣ K$ divi…

math.AG2019

Generalization of Abhyankar's Lemma to henselian valued fields

Arpan Dutta

Abhyankar showed that for a finite tame extension $L_{1} / K$ and a finite extension $L_{2} / K$ of $P$ -adic fields, the condition $[ν L_{1} : ν K]$ divides $[ν L_{2} : ν K]$ is suffici…