On the deviations of a \(\mathbb{Q}\)-algebra
type: Item
instance of: scholarly article
title: On the deviations of a \(\mathbb{Q}\)-algebra
zbMATH Open document ID: 0769.55009
DOI: 10.1016/0022-4049(93)90141-F
author: Nicolas Dupont
published in: Journal of Pure and Applied Algebra
publication date: 1993-05-16T00:00:00Z
review text: The study of the rational homotopy type of 1-connected spaces is related to the study of local rings. From this point of view, to the graded commutative algebra \(H = H^*(X;\mathbb{Q})\) is naturally associated the series \[ \sum^ \infty_{j=0}\dim\text{Tor}^ H_ j(\mathbb{Q},\mathbb{Q})t^ j = \prod^ \infty_{i=0}{(1+t^{2i+1})^{\varepsilon_{2i}}\over (1-t^{2i+2})^{\varepsilon_{2i+1}}} \] and the Gulliksen-Levin conjecture translates to: If \(H\) is Noetherian and \(\varepsilon_ i = 0\) for some \(i \geq 2\) then all \(\varepsilon_ i\) are zero for \(i \geq 2\). The author proves this conjecture when \(H\) has finite cuplength.
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 16E99
Mathematics Subject Classification ID: 16L99
zbMATH DE Number: 167299
zbMATH Keywords: rational homotopy type of 1-connected spaces
zbMATH Keywords: local rings
zbMATH Keywords: Gulliksen- Levin conjecture
reviewed by: Jean-Claude Thomas
MaRDI profile type: Publication
cites work: Free Lie Subalgebras of the Cohomology of Local Rings
cites work: Q3715232
cites work: Rational L.-S. Category and Its Applications
cites work: The radius of convergence of Poincaré series of loop spaces
cites work: Q5610428
cites work: Lectures on minimal models
cites work: Torsion gaps in the homotopy of finite complexes
cites work: Torsion gaps in the homotopy of finite complexes. II
cites work: The non-vanishing of the deviations of a local ring
cites work: Obstructions to homotopy equivalences
cites work: Infinitesimal computations in topology
full work available at URL: 0022-4049(93)90141-f
OpenAlex ID: W2092702073
description: scientific article; zbMATH DE number 167299