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Geometric models for higher Grothendieck-Witt groups in A1-homotopy theory
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In this article, it was shown that the higher Grothendieck-Witt groups, a.k.a. algebraic hermitian K-groups, are represented by an infinite orthogonal Grassmannian in the A1homotopy category of smooth schemes over a regular base for which 2 is a unit in the ring of regular functions.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.read more
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Simplicial homotopy theory
Paul G. Goerss,John F. Jardine +1 more
TL;DR: Simplicial sets, model categories, and cosimplicial spaces: applications for homotopy coherence, results and constructions, and more.
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$A^1$-homotopy theory of schemes
Fabien Morel,Vladimir Voevodsky +1 more
TL;DR: In this article, the authors present a legal opinion on the applicability of commercial or impression systématiques in the context of the agreement of the publication mathématique de l'I.H.É.S.
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Homotopy colimits in the category of small categories
TL;DR: In this article, Quillen and Waldhausen define a higher algebraic K-theory by taking homotopy groups of the classifying spaces of certain categories, which can then be used for geometric topology.