Acta Mathematica

Examples of finite free complexes of small rank and small homology

Srikanth B. Iyengar and Mark E. Walker

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Abstract

This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying free modules, or the total length of their homology, is less than predicted by various conjectures in the theory of transformation groups and in local algebra.

Article information

Source
Acta Math., Volume 221, Number 1 (2018), 143-158.

Dates
Received: 7 June 2017
Revised: 17 February 2018
First available in Project Euclid: 19 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.acta/1560966803

Digital Object Identifier
doi:10.4310/ACTA.2018.v221.n1.a4

Mathematical Reviews number (MathSciNet)
MR3877020

Zentralblatt MATH identifier
1403.13026

Subjects
Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13D22: Homological conjectures (intersection theorems) 55M35: Finite groups of transformations (including Smith theory) [See also 57S17] 57S17: Finite transformation groups

Keywords
complete intersection ring finite free complex total Betti number toral rank conjecture

Citation

Iyengar, Srikanth B.; Walker, Mark E. Examples of finite free complexes of small rank and small homology. Acta Math. 221 (2018), no. 1, 143--158. doi:10.4310/ACTA.2018.v221.n1.a4. https://projecteuclid.org/euclid.acta/1560966803


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