${\mathbb{P}}^1$-gluing for 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 $2n\ge d+3$.

21 pages. arXiv admin note: substantial text overlap with arXiv:1701.00509. v2: Thoroughly revised and expanded, fixed some mistakes from the earlier version. Comments are very much welcome! 23 pages