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On very effective hermitian K-theory

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HHHW02 - Equivariant and motivic homotopy theory

We argue that the very effective cover of hermitian K-theory in the sense of motivic homotopy theory is a convenient algebro-geometric generalization of the connective real topological K-theory spectrum. This means the very effective cover acquires the correct Betti realization, its motivic cohomology has the desired structure as a module over the motivic Steenrod algebra, and that its motivic Adams and slice spectral sequences are amenable to calculations. The latter applies to provide the expected connectivity for its unit map from the motivic sphere spectrum. This is joint work with Alexey Ananyevskiy and Paul Arne Ostvaer.

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

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