Hermitian K-theory, derived equivalences and Karoubi's fundamental theorem
By M. Schlichting. 2012
87 citations recorded by the source corpus.
Abstract 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 generalisation of Karoubi's Fundamental Theorem. For the higher Grothendieck–Witt groups of vector bundles of (possibly singular) schemes X with an ample family of line-bundles such that 1 2 ∈ Γ ( X , O X ) , we obtain Mayer–Vietoris long exact sequences for Nisnevich coverings and blow-ups along regularly embedded centres, 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/043b7cb94d2c5719911334a5c1255d820f6cef0a
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Slices of hermitian $K$–theory and Milnor's conjecture on quadratic forms (2013, methodology): “dimensional regular noetherian base scheme Sequipped with the trivial involution and with 2 invertible in its ring of regular functions, i.e., 1 2 ∈Γ(S,OS). A closely related statement is obtained in [49]. The sequence (5) is employed in our computation of the slices of KQ. The algebraic K-theory sp”