Hermitian $K$-theory and Milnor-Witt motivic cohomology over $\mathbb Z$

Håkon Kolderup; Oliver Röndigs; Paul Arne Østvær

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arXiv · 2509.16404

Hermitian $K$-theory and Milnor-Witt motivic cohomology over $\mathbb Z$

Håkon Kolderup·Oliver Röndigs·Paul Arne Østvær

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Abstract

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.

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BibTeX RIS

Håkon Kolderup, Oliver Röndigs, Paul Arne Østvær. 2025-09-19. Hermitian $K$-theory and Milnor-Witt motivic cohomology over $\mathbb Z$. https://arxiv.org/abs/2509.16404

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