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Hermitian K-theory of stable infinity categories

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

I wil report on joint work with E. Dotto, Y. Harpaz, F. Hebestreit, M. Land, K. Moi, D. Nardin, T. Nikolaus and W. Steimle about Hermitian K-theory in the context of stable infinity categories. I’ll try to explain why this framework has many advantages in terms of flexibility and naturality, and how it enabled us to solve open conjectures such as Karoubi periodicity. The relevance to motives is that hermitian K-theory appears as endomorphisms of the point in SH via a famous theorem of Morel, and that our approach removes any invertibility of 2 assumption related to Hermitian K-theory, and should thus help to remove this assumption in various motivic results.

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

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