Monday, September 19, 2022 3:30pm to 4:30pm
About this Event
3620 South Vermont Avenue, Los Angeles, CA 90089
Brian Shin, UCLA
Abstract: 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 $\mathcal{SH}(S)$ 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 norm monoidal structures on various extensions of motivic homotopy theory where the spaces/spectra are equipped with (generalized) 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 Elmanto--Hoyois--Khan--Sosnilo--Yakerson.
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