Grothendieck-Witt groups
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General Introduction
See also Chow-Witt groups
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Search results
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Online References
Walter: Grothendieck-Witt groups of triangulated cats.
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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.
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Other Information
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