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The slices of KGL over arbitrary bases

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KA2W01 - Algebraic K-theory, motivic cohomology and motivic homotopy theory

I will explain how to prove that, over any base scheme whatsover, the slices (in the sense of Voevodsky) of the motivic spectrum KGL (representing homotopy algebraic K-theory) coincide with Spitzweck’s motivic cohomology. This affirms a conjecture of Voevodsky. As an application, over any scheme of finite valuative dimension one obtains a well-behaved spectral sequence from motivic cohomology to homotopy K-theory. Thus we find in great generality a conceptual construction of the “motivic spectral sequence”.

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

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