Hermitian K-theory of quadric hypersurfaces
Heng Xie
TL;DR
This paper investigates the Hermitian K-theory of quadric hypersurfaces over rings where 2 is invertible, establishing fibration sequences that connect it to the base ring and Clifford algebras with dualities.
Contribution
It introduces new fibration sequences relating Hermitian K-theory of quadrics to Clifford algebras and base rings, considering all shifts and twists.
Findings
Established fibration sequences linking Hermitian K-theory to Clifford algebras.
Accounted for all shifts and twists in the Hermitian K-theory framework.
Connected Hermitian K-theory of quadrics with algebraic structures over rings.
Abstract
Let k be a commutative ring in which 2 is invertible. We prove that the Hermitian K-theory of quadric hypersurfaces over k admits fibration sequences relating it to the base ring and to Clifford algebras equipped with various duality coefficients. All shifts and twists are taken into account.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology