Abstract :
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.
