Grigory Garkusha (Swansea): Framed correspondences, part IFramed correspondences were invented and studied by Voevodsky in the early 2000-s, aiming at the construction of a new model for motivic stable homotopy theory. Joint with Ivan Panin we introduce and study framed motives of algebraic varieties basing on Voevodsky's framed correspondences. Framed motives allow to construct an explicit model for the suspension P1-spectrum of an algebraic variety. Framed correspondences also give a kind of motivic infinite loop space machine. They also lead to several important explicit computations such as rational motivic homotopy theory or recovering the celebrated Morel theorem that computes certain motivic homotopy groups of the motivic sphere spectrum in terms of Milnor-Witt K-theory. In these lectures we shall discuss basic facts on framed correspondences and related constructions.
Published Sep. 27, 2017 11:44 AM - Last modified Sep. 27, 2017 11:44 AM