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Karoubi-Grothendieck-Witt spectra

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HHHW06 - HHH follow on: Homotopy: fruit of the fertile furrow

jt with B.Calmès, E.Dotto, Y.Harpaz, K.Moi, M.Land, D.Nardin, T.Nikolaus and W.Steimle I will explain an analogue of the fundamental fibre sequence relating connective K-, Grothendieck-Witt- and L-spectra that involves non-connective K-theory and the Karoubi-Grothendieck-Witt-spectra of the title. It is this version of Grothendieck-Witt spectra that satisfy Zariski (even Nisnevich) descent, and as part of the identification of the appropriate version of L-spectra, I will give a unification of the Bass-Heller-Swan and Shaneson splittings in K- and L-theory, respectively, that also allows for the computation of Grothendieck-Witt groups of Laurent polynomial rings.

This talk is part of the Isaac Newton Institute Seminar Series series.

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