132.199.243.28: Created page with "In recent joint work with Calmès, Dotto, Harpaz, Land, Moi, Nardin and Nikolaus we developed a formalism for Grothendieck-Witt spectra of stable categories, that is very amen..."

2022-05-06T15:04:27Z

Created page with "In recent joint work with Calmès, Dotto, Harpaz, Land, Moi, Nardin and Nikolaus we developed a formalism for Grothendieck-Witt spectra of stable categories, that is very amen..."

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In recent joint work with Calmès, Dotto, Harpaz, Land, Moi, Nardin and Nikolaus we developed a formalism for Grothendieck-Witt spectra of stable categories, that is very amenable to computation, in particular enjoying a tight relation to Witt-(or L-)spectra. After briefly recalling the set-up, I will explain how this theory recovers the classical Grothendieck-Witt animae of ordinary rings, which are defined as group completions of moduli spaces of unimodular forms over R. In combination these statements allow us to solve a number of open problems, and allow access to the stable homology of orthogonal and symplectic groups over the integers for example.

The comparison itself is a hermitian analogue of Quillen's `+=Q´ theorem and the Gillet-Waldhausen theorem, though our proof proceeds very differently: It is based on ideas from the theory of cobordism categories in manifold topology, of which we provide an algebraic analog based on Ranicki's algebraic surgery theory.

Stable moduli spaces of hermitian forms - Revision history

132.199.243.28: Created page with "In recent joint work with Calmès, Dotto, Harpaz, Land, Moi, Nardin and Nikolaus we developed a formalism for Grothendieck-Witt spectra of stable categories, that is very amen..."