The Motivic Brouwer Degree

Explore a comprehensive lecture on the motivic Brouwer degree presented by Fabien Morel from University LMU Munich as part of the 2024 Program on Motivic Homotopy Theory at the Park City Mathematics Institute. Delve into advanced mathematical concepts that bridge classical homotopy theory with modern algebraic geometry, building upon the groundbreaking work of Morel and Voevodsky from the 1990s. Learn how motivic homotopy theory serves as a powerful tool for understanding arithmetic aspects in algebra and algebraic geometry while examining its fascinating development as a generalization of classical homotopy theory. Gain insights into unstable motivic homotopy theory, characteristic classes, enumerative geometry, and Weil conjectures in motivic homotopy theory. Requires foundational knowledge of algebraic geometry, algebraic topology, and homotopy theory, with additional background in Galois cohomology and étale cohomology being beneficial.