Localization of complete intersections

TL;DR

This paper provides a straightforward proof that localizing an abstract complete intersection at a prime ideal results in another abstract complete intersection, simplifying previous complex proofs.

Contribution

It offers an elementary proof of Avramov's result on the localization of complete intersections, enhancing understanding and accessibility.

Findings

Localization preserves the complete intersection property.

Elementary proof simplifies previous complex arguments.

Supports broader applications in algebraic geometry and commutative algebra.

Abstract

Let $(A,\mathfrak{m})$ be an abstract complete intersection and let $P$ be a prime ideal of $A$. In [1] Avramov proved that $A_P$ is an abstract complete intersection. In this paper we give an elementary proof of this result.