Curve selection lemma in arc spaces

TL;DR

This paper generalizes the curve selection lemma for Noetherian schemes and applies it to arc spaces, providing new versions and answering an open question in the field.

Contribution

It introduces a generalized curve selection lemma for arc spaces and leverages a structure theorem to derive multiple versions, advancing understanding in algebraic geometry.

Findings

Proved a version of the Curve Selection Lemma in arc spaces

Answered affirmatively a question by Reguera

Derived additional versions using a structure theorem

Abstract

We first generalize a curve selection lemma for Noetherian schemes and apply it to prove a version of Curve Selection Lemma in arc spaces, answering affirmatively a question by Reguera. Furthermore, thanks to a structure theorem of Grinberg, Kazhdan and Drinfeld, we obtain other versions of Curve Selection Lemma in arc spaces.