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.

Share this page:

Contact details

Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH
United Kingdom

Tel.: +44 (0)116 229 7407

Campus Based Courses

Undergraduate: mathsug@le.ac.uk
Postgraduate Taught: mathspg@le.ac.uk

Postgraduate Research: pgrmaths@le.ac.uk

Distance Learning Course  

Actuarial Science:

DL Study

Student complaints procedure

DisabledGo logo

The University of Leicester is committed to equal access to our facilities. DisabledGo has detailed accessibility guides for College House and the Michael Atiyah Building.