Cotangent functors and Herzog's last theorem

TL;DR

This paper explores cotangent functors and their relation to Herzog's conjecture, proposing a connection between cotangent functor vanishing and complete intersection properties in algebraic geometry.

Contribution

It introduces a new perspective on cotangent functors based on Palamodov's approach and formulates a conjecture linking these functors to complete intersections.

Findings

Proposes a conjecture relating cotangent functors to complete intersections.

Develops a theoretical framework for cotangent functors following Palamodov.

Suggests potential criteria for identifying complete intersections via cotangent functors.

Abstract

We present the theory of cotangent functors following the approach of Palamodov, and a conjecture of Herzog relating the vanishing of certain cotangent functors to the property of being a complete intersection.