Half twists of Hodge structures of CM-type

Abstract

To a Hodge structure V of weight k with CM by a field K we associate Hodge structures V_-n/2 of weight k+n for n positive and, under certain circumstances, also for n negative. We show that these 'half twists' come up naturally in the Kuga-Satake varieties of weight two Hodge structures with CM by an imaginary quadratic field