WiSe 22/23: Motivic homotopy theory

Lectures: Friday 12-14 M102
Exercises: Friday 14-16 M102

Motivic homotopy theory was developed by F. Morel and V. Voevodsky in the late 90s in order to “do homotopy theory” with algebraic varieties. This course will introduce the basic definitions from a modern perspective and present some of the foundational results (such as the purity and localization theorems) that one needs to get started. Time permitting, the stable theory will be introduced, with a view towards the formalism of six operations.

References

The original article of Morel and Voevodsky (the foundational material is now largely outdated):

• F. Morel and V. Voevodsky, A¹-homotopy theory of schemes, 1999

A useful “primer” covering the basic theory, examples and some applications:

• B. Antieau and E. Elmanto, A primer for unstable motivic homotopy theory, 2016

Voevodsky and Morel’s ICM addresses:

• V. Voevodsky, A¹-homotopy theory, 1998
• F. Morel, A¹-algebraic topology, 2006