# 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.

Published Sep. 13, 2022 1:19 PM - Last modified Oct. 18, 2022 10:00 AM