Midwest Algebra, Geometry and their Interactions Conference MAGIC05 University of Notre Dame, Notre Dame October 7-11, 2005 Regularity of powers of ideals by Marc CHARDIN, Jussieu - Paris VI Abstract: The behaviour of the Castelnuovo-Mumford regularity of different types of powers of ideals, or of ideal sheaves, has been recently investigated by several authors. We will present results on the regularity of symbolic powers, Frobenius powers, and ordinary powers. These results have all in common variations on a lemma from the article of Gruson, Lazarsfeld and Peskine on the regularity of curves. Closely related applications to regularity of Tor modules, as initiated by Eisenbud, Huneke and Ulrich, or to the implicitization problem, in the framework of Busé and Jouanolou approach using approximation complexes, will be given.