3:45 pm Tuesday, May 5, 2020
Junior Geometry: The Grothendieck ring (spectrum) of varieties by
Arun Debray [mail] (UT Austin) in Zoom
The Grothendieck ring of a category is an invariant built by splitting extensions; one standard example is built from the category of algebraic varieties over a field k. In certain standard settings, the Grothendieck ring of a category generalizes to a series of abelian groups, or even a spectrum in the sense of homotopy theory, and this stronger invariant buys you additional information. The category of varieties doesn't fit into these standard settings, but work of Campbell and Zakharevich shows how to produce a ring spectrum out of it nonetheless, and gives some applications. In this talk, I'll discuss some of the context of their work, their new construction, and why I think these applications are cool. Submitted by
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