2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59705To 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.16 pages. To appear in: Journal of the Mathematical Society of JapanAlgebraic Geometrytext