S. Mishra

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math.AC2025

A Class of simple derivations of polynomial ring $k [x_{1}, x_{2}, \dots, x_{n}]$

Sumit Chandra Mishra, Dibyendu Mondal, Pankaj Shukla

Let $k$ be a field of characteristic zero. Let $m$ and $I^\pm$ be positive integers. For $n \geq 2$ , let $R_{n} = k [x_{1}, x_{2}, \dots, x_{n}]$ with the $k$ -derivation $d_{n}$ given by $d_n=(1-x_1x_…

math.AC2025

On the Isotropy Groups of Non-Invertible Simple Derivations

Sumit Chandra Mishra, Dibyendu Mondal, Pankaj Shukla

Let $k$ be a field of characteristic zero, and let $i$ and $n$ be positive integers with $i \geq 2$ and $n > i$ . Consider a non-invertible $k$ -derivation $d_{i}$ of the polynomial ring…

math.AC2025

A ruled residue theorem for function fields of hyperelliptic curves

Parul Gupta, Sumit Chandra Mishra

We study residually transcendental extensions of a valuation $v$ on a field $E$ to function fields of hyperelliptic curves over $E$ . We show that $v$ has at most finitely many exte…

A Class of simple derivations of polynomial ring k[x1​,x2​,…,xn​]

On the Isotropy Groups of Non-Invertible Simple Derivations

A ruled residue theorem for function fields of hyperelliptic curves

A Class of simple derivations of polynomial ring $k [x_{1}, x_{2}, \dots, x_{n}]$