${\mathbb P}^1$-gluing for local complete intersections

TL;DR

This paper extends the Affine Horrocks' Theorem to local complete intersection ideals in polynomial rings over regular domains, under specific dimension and characteristic conditions.

Contribution

It provides a new analogue of the Affine Horrocks' Theorem for local complete intersection ideals in polynomial rings over regular domains.

Findings

Proves the analogue under specified dimension and characteristic conditions

Extends the applicability of Horrocks' Theorem to a broader class of ideals

Establishes conditions for the theorem in the context of local complete intersections

Abstract

We prove an analogue of the Affine Horrocks' Theorem for local complete intersection ideals of height $n$ in $R[T]$, where $R$ is a regular domain of dimension $d$, which is essentially of finite type over an infinite perfect field of characteristic unequal to $2$, and $2n\geq d+3$.