Acta Mathematica

Volume 221 (2018)

Number 1

Examples of finite free complexes of small rank and small homology

Pages: 143 – 158



Srikanth B. Iyengar (Department of Mathematics, University of Utah, Salt Lake City, Ut. U.S.A.)

Mark E. Walker (Department of Mathematics, University of Nebraska, Lincoln, Ne., U.S.A.)


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.


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

2010 Mathematics Subject Classification

Primary 13D02. Secondary 13D22, 55M35, 57S17.

Received 7 June 2017

Received revised 17 February 2018

Accepted 2 May 2018

Published 6 November 2018