Introduction to motivic homotopy theory

par Leonardo Colombo

lundi 15 juin 2026, 16:30 → 17:30 Europe/Paris

S435 (UMPA)

Motivic homotopy theory studies algebraic geometry by importing techniques from algebraic topology. It started in 1998 with V. Voevodsky's idea to do homotopy theory with algebraic varieties by replacing the unit interval [0,1] with the affine line A^1. In this talk, following analogies with algebraic topology, we introduce A^1-homotopies, the category of motivic spaces, motivic spheres and motivic homotopy groups. We conclude by mentioning the stable motivic homotopy category SH. No previous knowledge of algebraic geometry is required.