arXiv subjects

Guillaume Pagot

Publications and source records attributed to Guillaume Pagot.

3 recordsLinked to original sources

arXiv2026

On the arithmetic and geometry of spaces $L_{m+1,n}$

Let $p$ be a prime number. Motivated by the local lifting problem for $(\mathbb{Z}/p\mathbb{Z})^n$ with $n>1$, we prove several new results on certain $\mathbb{F}_p$-vector spaces of logarithmic differential forms on the projective line in characteristic $p$, called "spaces $L_{m+1,n}$". Expanding the previous work by the first two authors, we prove positive and negative results for the existence of spaces $L_{m+1,n}$ in many situations. Moreover, we classify all spaces $L_{4p,2}$ for any $p$, and all spaces $L_{15,2}$ for $p=3$. Among the novel tools we use, Moore determinants and computational algebra play a prominent role.

math.NT↗

arXiv2024

The local lifting problem for $(\mathbb{Z}/2\mathbb{Z})^3$

Let $k$ be an algebraically closed field of characteristic $2$. In this paper we describe the $(\mathbb{Z}/2\mathbb{Z})^3$-actions on $k[[z]]$ for which there is a discrete valuation ring $R$, a finite extension of the ring of Witt vectors $W(k)$, such that they can be lifted as a group of $R$-automorphisms of $R[[Z]]$. In fact the necessary and sufficient condition for such an action to lift involves only the conductor type of the corresponding extension.

math.AG↗

arXiv2002

$F_p$-espaces vectoriels de formes différentielles logarithmiques sur la droite projective

Let k be an algebraically closed field of characteristic p >0. Let $m \in \N$, (m,p)=1. We study $\fp$-vector spaces of logarithmic differential forms on the projective line such that each non zero form has a unique zero at $\infty$ of given order m-1. We discuss the existence of such vectors spaces according to the value of m. We give applications to the lifting to characteristic 0 of $(\Z /p\Z)^n$ actions as k-automorphisms of $k[[t]]$.

math.NT↗