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Friday, February 4, 2022 - 2:00pm

Shay Ben Moshe

Hebrew University of Jerusalem


University of Pennsylvania


The redshift conjecture of Ausoni-Rognes says that there is a strong interaction between algebraic K-theory and the chromatic filtration on spectra. Namely, that if a ring spectrum R is of chromatic height n, then K(R) is of chromatic height n+1. Hopkins-Lurie, followed by Carmeli-Schlank-Yanovski, showed that the category of spectra of height n is higher semiadditive, that is, colimits and limits indexed by pi-finite spaces are canonically equivalent. In this talk we will describe higher semiadditive K-theory, a variant of algebraic K-theory that takes higher semiadditivity into account. We will explain how semiadditive methods allow us to show that it satisfies a form of the redshift conjecture. Relevant background on algebraic K-theory, chromatic homotopy and semiadditivity will be explained.