A Remark on Higher Homotopy Sheaves of Derived Arc Spaces

TL;DR

This paper examines higher homotopy sheaves of derived arc spaces, showing they coincide with classical arc spaces for reduced local complete intersection schemes, extending previous results for smooth schemes.

Contribution

It demonstrates that derived arc spaces do not differ from classical ones for reduced local complete intersection schemes, generalizing earlier findings for smooth schemes.

Findings

Derived arc spaces match classical arc spaces for reduced local complete intersection schemes.

Higher homotopy sheaves of derived arc spaces are trivial in this context.

Extends known results from smooth schemes to a broader class of schemes.

Abstract

In their work, \cite{GR}, Gaitsgory and Rozenblyum introduce a derived version of the well-studied arc spaces of classical algebraic geometry. They observe that these derived spaces do not differ from their classical counterparts in the case of smooth schemes. In this note we will see that this is also the case for reduced local complete intersection schemes