Ramification of inseparable coverings of schemes and application to diagonalizable group actions

TL;DR

This paper introduces a formalism for inseparable coverings of schemes and applies it to derive a Riemann-Hurwitz type formula for torsors under infinitesimal diagonalizable group schemes.

Contribution

It defines inseparable coverings of schemes and develops a ramification theory, extending classical concepts to new algebraic geometric contexts.

Findings

Established a formalism for inseparable coverings

Derived a Riemann-Hurwitz type formula for specific torsors

Extended classical ramification theory to infinitesimal group schemes

Abstract

We define the notion of inseparable coverings of schemes and we propose a ramification formalism for them, along the lines of the classical one. Using this formalism we prove a formula analogous to the classical Riemann-Hurwitz formula for generic torsors under infinitesimal diagonalizable group schemes.