Oct 24 – 28, 2022
Louvre Lens Vallée
Europe/Paris timezone
À l'occasion du 64ème anniversaire de Bruno Kahn

Representability of Hermitian K-theory in the homotopy category of schemes

Oct 27, 2022, 11:00 AM
Louvre Lens Vallée

Louvre Lens Vallée

84 Rue Paul Bert, 62300 Lens


Baptiste Calmes


This is a report on joint work with Yonatan Harpaz and Denis Nardin.

Hermitian K-theory and motivic homotopy theory enjoy a fruitful relationship, in particular through the quadratic nature of morphisms in the latter, epistomized by the theorem of Morel relating the endomorphisms of the unit sphere with Milnor-Witt K-theory.

A recent definition of Hermitian K-theory in terms of stable infinity-categories and quadratic functors enables one to consider various flavours of Hermitian K-theory -- symmetric forms, quadratic forms, etc. -- related in a common framework. As required to distinguish these, the theory unfolds nicely without any invertibility of 2 assumption.

I'll discuss representability results of Hermtian K-theory in the stable homotopy category of schemes over a base, in a characteristic free manner.

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