arXiv subjects

Poulami Mandal

Publications and source records attributed to Poulami Mandal.

2 recordsLinked to original sources

arXiv2026

The minimum genus of Galois covers of curves

Let $Y\longrightarrow X$ be a $G$-Galois connected cover of smooth projective curves over an algebraically closed field $k$ of positive characteristic $p$ with the branch locus contained in a finite subset of closed points $S_X$ in $X$, where $G$ is a finite cyclic $p$-group and $l$ is a prime number other than $p$. Let $\Gamma$ be an extension of an elementary abelian $l$-group $H$ by $G$. We find $G$-stable submodules of $l$-torsion of the Picard group of $Y$ and its generalisation. This is used to describe a method for finding the minimum genus of $\Gamma$-covers of $X$, \'etale over $X\setminus S_X$, dominating $Y$; and also the minimum of the genera of $\Gamma$-covers of $\mathbb{P}^1$ \'etale over $\mathbb{A}^1$.

math.AG↗

arXiv2024

A criterion for solving embedding problems for the etale fundamental group of curves

Let $C$ be an affine curve over an algebraically closed field $k$ of characteristic $p>0$. Given an embedding problem $(β:Γ\longrightarrow G, α: π^{et}_1(C)\longrightarrow G)$ for $π_1^{et}(C)$ where $β$ is a surjective homomorphism of finite groups with prime-to-$p$ kernel $H$, we discuss when an $H$-cover of the $G$-cover of $C$ corresponding to $α$ is a solution. When $H$ is abelian and $G$ is a $p$-group, some necessary and sufficient conditions for the solvability of the embedding problem are given in terms of the action of $G$ on certain generalized Picard group.

math.AG↗