Higher $K$-theory of forms III: from chain complexes to derived categories

We exhibit a canonical equivalence between the hermitian $K$-theory (alias Grothendieck-Witt) spectrum of an exact form category and that of its derived Poincar\'e $\infty$-category, with no assumptions on the invertibility of $2$. Along the way, we obtain a model for the nonabelian derived fun...

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Bibliographic Details
Main Authors:	Marlowe, Daniel, Schlichting, Marco
Format:	Journal Article
Language:	English
Published:	14-11-2024
Subjects:	Mathematics - K-Theory and Homology
Online Access:	Get full text
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Summary:	We exhibit a canonical equivalence between the hermitian $K$-theory (alias Grothendieck-Witt) spectrum of an exact form category and that of its derived Poincar\'e $\infty$-category, with no assumptions on the invertibility of $2$. Along the way, we obtain a model for the nonabelian derived functor of a nondegenerate quadratic functor on an exact category.
DOI:	10.48550/arxiv.2411.09401