The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes
By M. Schlichting. 2008
70 citations recorded by the source corpus.
We prove localization and Zariski-Mayer-Vietoris for higher Gro-thendieck-Witt groups, alias hermitian K-groups, of schemes admitting an ample family of line-bundles. No assumption on the characteristic is needed, and our schemes can be singular. Along the way, we prove Additivity, Fibration and Approximation theorems for the hermitian K-theory of exact categories with weak equivalences and duality.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/989f2563e74b37a33cc964c323d1adca572eae90
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Geometric models for higher Grothendieck-Witt groups in A1-homotopy theory (2013, background): “The extension to non-affine schemes follows from [14] and is”
- On Stably Free Modules over Affine Algebras (2011, methodology): “eliminaries. In this section, we recalla few basicfactsabout GrothendieckWitt groups. These are a modern version of Hermitian K-theory. The general reference here is the work of M. Schlichting ([29], [30]). Since we use GrothendieckWitt groups only for affine schemes, we restrict to this case. Let Rbe”
- The generalized slices of Hermitian K‐theory (2016, unknown): “By Bott periodicity, we have GW [ n +4] GW [ n ] and so KO [ n +4] KO [ n ] [ 22 , Proposition 7].”
- Splitting vector bundles outside the stable range and A^1-homotopy sheaves of punctured affine spaces (2012, background): “n). As Hornbostel remarks [Hor05, Remark 3.8], the analogous proof with B•GLnreplaced by B•Sp 2n (replace references to Thomason’s results in [MV99] by the corresponding results due to Schlichting in [Sch10] and use the fact that Sp 2n is a special group, i.e., that all Sp 2n-torsors over smooth sch”