Adequate complete intersection homomorphisms

TL;DR

This paper investigates three classes of local homomorphisms that lie between complete intersection and quasi-complete intersection types, analyzing their behavior concerning the ascent and descent of the complete intersection property.

Contribution

It introduces and studies three new classes of local homomorphisms that address limitations of existing classes, enhancing understanding of the complete intersection property.

Findings

Identifies properties of the three classes regarding ascent and descent

Shows how these classes interpolate between known homomorphism classes

Provides insights into the structure of local homomorphisms with respect to complete intersections

Abstract

We study three classes of local homomorphisms and their behavior with respect to the ascent and descent of the \emph{complete intersection} property. Crucially, they fall in between the already studied classes of complete intersection and quasi-complete intersection homomorphisms, while also repairing some of the issues these presented.