Arpan Dutta

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20192021

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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.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…