Niels Feld (Toulouse): From motivic homotopy theory to birational geometry

This talk was part of the workshop "Motivic and non-commutative aspects of enumerative geometry" held in July 2023 at Radboud University, Nijmegen, The Netherlands.

Abstract: In this talk, I will start with some general background in motivic homotopy theory, and study in particular the heart of the stable motivic homotopy category of Morel and Voevodsky. Then I will present some consequences of the theory of Milnor-Witt cycle modules and their associated Chow-Witt groups in birational geometry. In the end, I will discuss a motivic formulation concerning the existence of rational points in a given variety and its link to the existence of 0-cycles of degree 1.