Periodic resolutions over exterior algebras

✍ Scribed by David Eisenbud

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 132 KB
• Volume: 258
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00511-2

✦ Synopsis

In this paper we study modules with periodic free resolutions (that is, periodic modules) over an exterior algebra. We show that any module with bounded Betti numbers (that is, a module whose syzygy modules have a bounded number of generators) must have periodic free resolution of period 2, and that for graded modules the period is 1. We also show that any module with a linear Tate resolution is periodic. We give a criterion of exactness for periodic complexes and a parameterization of the set of periodic modules.