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HIGHER $K$-THEORY OF FORMS I. FROM RINGS TO EXACT CATEGORIES

Part of: Forms and linear algebraic groups Higher algebraic $K$-theory $K$-theory of forms

Published online by Cambridge University Press:  02 August 2019

Marco Schlichting Open the ORCID record for Marco Schlichting [Opens in a new window]
Marco Schlichting*
Affiliation:
Marco Schlichting, Mathematics Institute, Zeeman Building, University of Warwick, CoventryCV4 7AL, UK (m.schlichting@warwick.ac.uk)
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Abstract

We prove the analog for the $K$-theory of forms of the $Q=+$ theorem in algebraic $K$-theory. That is, we show that the $K$-theory of forms defined in terms of an $S_{\bullet }$-construction is a group completion of the category of quadratic spaces for form categories in which all admissible exact sequences split. This applies for instance to quadratic and hermitian forms defined with respect to a form parameter.

Keywords

higher K-theory of formsgroup completion

MSC classification

Primary: 19G38: Hermitian $K$-theory, relations with $K$-theory of rings
Secondary: 19D06: $Q$- and plus-constructions 11E70: $K$-theory of quadratic and Hermitian forms
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 4 , July 2021 , pp. 1205 - 1273
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Copyright
© The Author(s), 2019. Published by Cambridge University Press

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