Title: On the K-theory of pushouts
Speaker: Markus Land
Speaker Info: LMU Munich
Brief Description: This talk is on Zoom. E-mail the organizer for the link if needed.
Special Note: Part of the Chicagoland Topology Series. Note unusual time.
I will report on joint work with Tamme. First, I will give a brief review of (a generalisation) of our previous theorem on the K-theory of pullbacks and indicate its use for studying properties like excision, nilinvariance, and cdh-descent. Then, I will explain how, under certain assumptions, we obtain a formula for the circle-dot ring appearing in our previous theorem, namely as a pushout of E_1-ring spectra. I will discuss some examples to illustrate that the resulting pushouts can often be calculated explicitly, and remark on natural questions that arose in this context about the K-theory of coconnective rings which have been solved by Burklund—Levy.Date: Tuesday, February 15, 2022