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

  • Marco Schlichting (a1)

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.

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