Andr\'e-Quillen homology and ascent of complete intersection flat dimensions

TL;DR

This paper uses Andre9-Quillen homology to establish ascent properties of complete intersection flat dimensions under certain local homomorphisms, extending previous results on Andre9-Quillen dimensions.

Contribution

It introduces a new ascent theorem for complete intersection flat dimensions via Andre9-Quillen homology, generalizing existing results to essentially finite type homomorphisms.

Findings

Proves ascent of complete intersection flat dimensions under specified conditions.

Extends results on Andre9-Quillen dimension to broader classes of homomorphisms.

Provides new tools for analyzing homological properties in algebraic geometry and commutative algebra.

Abstract

Using Andr\'{e}-Quillen homology, we prove an ascent result for different types of complete intersection flat dimensions along an essentially of finite type flat local homomorphism with complete intersection closed fiber. As an application of our result, we extend a result of Majadas Soto and of Avramov, Henriques and \c{S}ega on the Andr\'{e}-Quillen dimension of surjective local homomorphisms to that of essentially of finite types.