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Main Authors:	Kolderup, Håkon, Röndigs, Oliver, Østvær, Paul Arne
Format:	Preprint
Published:	2025
Subjects:	Algebraic Geometry Algebraic Topology K-Theory and Homology
Online Access:	https://arxiv.org/abs/2509.16404
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author	Kolderup, Håkon Röndigs, Oliver Østvær, Paul Arne
author_facet	Kolderup, Håkon Röndigs, Oliver Østvær, Paul Arne
contents	The theme of this paper is to compute hermitian $K$-groups in terms of the recently developed theory of Milnor-Witt motivic cohomology. Our approach makes use of the very effective slice spectral sequence within the motivic stable homotopy category, which we analyze in detail for base schemes of arithmetic interest. We show a Grothendieck-Riemann-Roch theorem, determine the map between Milnor-Witt and hermitian $K$-theory up to degree five for all fields, and compute the hermitian $K$-groups and the higher Witt-groups of the ring of integers.
format	Preprint
id	arxiv_https___arxiv_org_abs_2509_16404
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Hermitian $K$-theory and Milnor-Witt motivic cohomology over $\mathbb Z$ Kolderup, Håkon Röndigs, Oliver Østvær, Paul Arne Algebraic Geometry Algebraic Topology K-Theory and Homology The theme of this paper is to compute hermitian $K$-groups in terms of the recently developed theory of Milnor-Witt motivic cohomology. Our approach makes use of the very effective slice spectral sequence within the motivic stable homotopy category, which we analyze in detail for base schemes of arithmetic interest. We show a Grothendieck-Riemann-Roch theorem, determine the map between Milnor-Witt and hermitian $K$-theory up to degree five for all fields, and compute the hermitian $K$-groups and the higher Witt-groups of the ring of integers.
title	Hermitian $K$-theory and Milnor-Witt motivic cohomology over $\mathbb Z$
topic	Algebraic Geometry Algebraic Topology K-Theory and Homology
url	https://arxiv.org/abs/2509.16404

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