A^1 enumerative geometry: counts of rational curves in P^2 - 2 of 2

Kirsten Wikelgren
Wed, Jun 12, 2019
PIMS, University of British Columbia
Workshop on Arithmetic Topology
We will introduce A^1 homotopy theory, focusing on the A^1 degree of Morel. We then use this theory to extend classical counts of algebraic-geometric objects defined over the complex numbers to other fields. The resulting counts are valued in the Grothendieck--Witt group of bilinear forms, and weight objects using certain arithmetic and geometric properties. We will focus on an enrichment of the count of degree d rational plane curves, which is joint work with Jesse Kass, Marc Levine, and Jake Solomon.


This is the second lecture in a two part series: part 1