Volume 221 (2018)
Examples of finite free complexes of small rank and small homology
Pages: 143 – 158
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