Finiteness of leaps of modules of integrable derivations of algebras of finite type

TL;DR

This paper proves the finiteness of leaps in modules of integrable derivations for finite type algebras over algebraically closed fields of positive characteristic, answering a key open question and establishing coherence of certain derivation modules.

Contribution

It demonstrates the finiteness of leaps for modules of integrable derivations and proves coherence of the module of infinite integrable derivations, advancing understanding in algebraic geometry.

Findings

Finiteness of leaps established for modules of integrable derivations.

Coherence of the module of ∞-integrable derivations proved.

Provides an affirmative answer to a question by L. Narváez Macarro.

Abstract

We prove the finiteness of leaps of modules of $m$-integrable derivations for algebras essentially of finite type and, more generally, for schemes essentially of finite type over an algebraically closed field of positive characteristic. This provides an affirmative answer to a question posed by L. Narv\'aez Macarro. As an application, we establish the coherence of the module of $\infty$-integrable derivations.