Geometric models for higher Grothendieck-Witt groups in A1-homotopy theory

2013/09/23 by Schlichting, Marco, Tripathi, Girja Shanker · 2 citations
#FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1309.5818

Abstract

We show that the higher Grothendieck-Witt groups, a.k.a. algebraic hermitian K-groups, are represented by an infinite orthogonal Grassmannian in the A1-homotopy category of smooth schemes over a regular base for which 2 is a unit in the ring of regular functions. We also give geometric models for various P1- and S1-loop spaces of hermitian K-theory.

Cited by

• Motivic homotopy theory for perfect schemes
• The nonexistence of sections of Stiefel varieties and stably free modules

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• A1-homotopy invariance of algebraic K-theory with coefficients and Kleinian singularities
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