Peter Arnd abstract

Title: Abstract Motivic Homotopy Theory

Abstract: We will start with an introduction to motivic homotopy theory for usual schemes, emphasizing the categorical constructions. Then we list some notions of "schemes over deeper bases" and other alternative settings of algebraic geometry where one would like to have a similar theory. 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 cartesian closed, presentable (infinity,1)-category and a commutative group object G therein (which plays the role of the multiplicative group scheme), we construct a classifying space for G-bundles, 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. While inspired from geometric constructions, all of these results are purely categorical.

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