Babylonian tower theorems on the punctured spectrum
type: Item
instance of: scholarly article
title: Babylonian tower theorems on the punctured spectrum
zbMATH Open document ID: 0541.14011
DOI: 10.1007/BF01455804
author: Hubert Flenner
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163961
review text: Horrocks has posed the following problem: Let \(...\to R_{n+1}\to R_ n\to...\to R_ 0\) be a ''tower'' of regular local rings, i.e. \(R_ n=R_{n+1}/(t_{n+1})\) for some nonzero divisor \(t_{n+1}\in R_{n+1}\). For every n, let \({\mathcal E}_ n\) be a vector bundle on the punctured spectrum of \(R_ n\) such that \({\mathcal E}_ n\) is the restriction of \({\mathcal E}_{n+1}\). Is then \({\mathcal E}_ n\) trivial for each n? In this paper an affirmative answer is given. Moreover, in most of the geometrically interesting cases there is a bound for how far \({\mathcal E}_ 0\) can be extended at most.- This generalizes results of Evans-Griffiths resp. Barth-Van de Ven, Sato and Tyurin in the projective case. The main idea of the proof consists in applying formal deformation theory. In the second part of the paper a similar result is derived for locally complete intersections on the punctured spectrum of a regular local ring.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14D15
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14M20
zbMATH DE Number: 3859282
zbMATH Keywords: tower of regular local rings
zbMATH Keywords: vector bundle on the punctured spectrum
zbMATH Keywords: formal deformation theory
zbMATH Keywords: locally complete intersections
MaRDI profile type: Publication
cites work: Q4119326
cites work: A decomposability criterion for algebraic 2-bundles on projective spaces
cites work: Lifting Syzygies and Extending Algebraic Vector Bundles
cites work: Filtering Cohomology and Lifting Vector Bundles
cites work: Ein Kriterium für vollständige Durchschnitte
cites work: Q5596003
cites work: Algebraic vector bundles on projective spaces: A problem list
cites work: Q4073477
cites work: ON EXTENDING VECTOR BUNDLES OVER PROJECTIVE SPACE
cites work: On the decomposability of infinitely extendable vector bundles on projective spaces and Grassmann varieties
cites work: Q4190741
cites work: Functors of Artin Rings
cites work: VECTOR BUNDLES OF FINITE RANK OVER INFINITE VARIETIES
OpenAlex ID: W1981134318
description: scientific article; zbMATH DE number 3859282