On tensor products of complete resolutions

Abstract

Abstract We construct tensor products of complete resolutions of finitely generated modules over Noetherian rings. As applications we prove that there exists complete resolutions over artinian Gorenstein rings whose sequence of negative Betti numbers grow exponentially, while the sequence of positive Betti numbers grow polynomially of any degree . We also describe complete resolutions of the simple module over groups algebras of elementary abelian groups and quantum complete intersections.