A-Upper Motives in Motivic Homotopy Theory

Watch a 59-minute lecture from the 2024 Program on Motivic Homotopy Theory where Professor Nikita Karpenko from the University of Alberta presents joint research with Charles de Clercq and Anne Quéguiner-Mathieu on extending results about motivic structure of projective homogeneous varieties under groups of inner type to arbitrary reductive groups. Delve into advanced concepts in motivic homotopy theory, which emerged from Morel and Voevodsky's work in the 1990s and has become instrumental in understanding arithmetic aspects of algebra and algebraic geometry. Part of the Graduate Summer School at PCMI (Park City Mathematics Institute), this lecture assumes foundational knowledge in algebraic geometry, algebraic topology, homotopy theory, and familiarity with Galois cohomology and étale cohomology is beneficial.