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Hermitian $$K$$-theory of exact categories. (English) Zbl 1328.19009
Summary: We study the theory of higher Grothendieck-Witt groups, alias algebraic hermitian $$K$$-theory, of symmetric bilinear forms in exact categories, and prove additivity, cofinality, dévissage and localization theorems - preparing the ground for the theory of higher Grothendieck-Witt groups of schemes as developed in the author’s papers [Invent. Math. 179, No. 2, 349–433 (2010; Zbl 1193.19005); “Hermitian $$K$$-theory, derived equivalences and Karoubi’s fundamental theorem”, preprint, http://www.math.lsu.edu/~mschlich/research/prelim.html]. No assumption on the characteristic is being made.

##### MSC:
 19G38 Hermitian $$K$$-theory, relations with $$K$$-theory of rings 19D06 $$Q$$- and plus-constructions 19G12 Witt groups of rings
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