Acta Mathematica

Examples of finite free complexes of small rank and small homology

Srikanth B. Iyengar and Mark E. Walker

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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