Holmstrom Grothendieck-Witt groups

Grothendieck-Witt groups

Walter: Grothendieck-Witt groups of triangulated cats.


Grothendieck-Witt groups

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Grothendieck-Witt groups

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Grothendieck-Witt groups

See also Chow-Witt groups


Grothendieck-Witt groups

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Grothendieck-Witt groups

arXiv:1209.0848 Hermitian K-theory, derived equivalences and Karoubi’s Fundamental Theorem from arXiv Front: math.KT by Marco Schlichting Within the framework of dg categories with weak equivalences and duality that have uniquely 2-divisible mapping complexes, we show that higher Grothendieck-Witt groups (aka. hermitian K-groups) are invariant under derived equivalences and that Morita exact sequences induce long exact sequences of Grothendieck-Witt groups. This implies an algebraic Bott sequence and a new proof and generalization of Karoubi’s Fundamental Theorem. For the higher Grothendieck-Witt groups of vector bundles of (possibly singular) schemes with an ample family of line-bundles such that 2 is invertible in the ring of regular functions, we obtain Mayer-Vietoris long exact sequences for Nisnevich coverings and blow-ups along regularly embedded centers, projective bundle formulas, and a Bass fundamental theorem. For coherent Grothendieck-Witt groups, we obtain a localization theorem analogous to Quillen’s K’-localization theorem.

nLab page on Grothendieck-Witt groups

Created on June 10, 2014 at 21:14:54 by Andreas Holmström