Algebra/Topology seminar

Speaker: Tom Bachmann

Title: Motivic versus topological homotopy classes

Abstract: I will report on joint work with Asok and Hopkins on the following question: if X and Y are motivic spaces (e.g., smooth varieties) over C, then one can consider both the motivic homotopy classes of maps between X and Y, as well as the classical homotopy classes of maps between the complex points X(C) and Y(C). Using the the Wilson space hypothesis (see
Hopkins' talk on Tuesday) as well as resolution theory (joint with Engelmann and Mattis) we exhibit a large class of examples of motivic spaces X, Y for which the motivic and topological homotopy classes actually coincide.