Brian Shin (UCLA) - Norms and Transfers in Motivic Homotopy Theory

Motivic homotopy theory is the study of homotopy-theoretic ideas in the setting of algebraic geometry. The basic categories of interest are those of motivic spaces \(\mathcal{H}(S)\) and motivic spectra \(\mathcal{H}(S)\) over a base scheme \(S\). In recent work of Bachmann-Hoyois, these categories were equipped with norm monoidal structures, variants of monoidal structures richer than what is usually the richest for homotopy theory (i.e. \(\mathbb{E}_\infty\)). In this talk, I will discuss a norm monoidal structure on an extension of motivic homotopy theory where the spaces/spectra are equipped with framed transfers. The construction of norms for motivic spaces with framed transfers will allow us to prove a norm monoidal enhancement of the motivic infinite loop space recognition principle of Elmnto-Hoyois-Khan-Sosnilo-Yakerson.