2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131997We investigate the behavior of Castelnuovo-Mumford regularity with respect to some classical functors : Tor, the Frobenius functor in positive characteristic, taking a power or a product (on ideals). These generalizes and refines previous results on these issues by several authors. As an application we provide results on the regularity of an intersection of subschemes of a projective scheme, under appropriate geometric hypotheses. Results on the rigidity of multiple Tor modules and on the characterization of their vanishing are given, motivated by geometric applications.Commutative AlgebraAlgebraic Geometry13D02; 13D07; 13D25; 13D45text