Algebra/Topology seminar by Peter Arndt

Algebra/Topology seminar by Peter Arndt (Düsseldorf)

Title: Motivic Homotopy Theory over deeper bases

Abstract: We start with a short reminder of (or introduction to) motivic homotopy theory for usual schemes. Then we list some notions of "schemes over deeper bases" and other alternative settings of algebraic geometry to motivate what follows. In the main part of the talk we present constructions and results generalizing those of motivic homotopy theory and working for a very general general input: Starting with a suitable infinity category and a commutative group object therein which plays the role of the multiplicative group scheme, we construct a Snaith type algebraic K-theory spectrum, Adams operations, rational splittings and a rational motivic Eilenberg-MacLane spectrum, all in a way that is compatible with base change.