What does this research mean for the field?

The cellular absolute motivic spectrum constructed via the geometry of orthogonal and hyperbolic Grassmannians coincides with the previously constructed motivic ring spectrum for representing hermitian K-theory. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to demonstrate that a constructed cellular absolute motivic spectrum matches another known motivic ring spectrum representing hermitian K-theory.

June 13, 2026Open Access

A Cellular Absolute Motivic Ring Spectrum Representing Hermitian K -Theory

Key Points

The aim is to demonstrate that a constructed cellular absolute motivic spectrum matches another known motivic ring spectrum representing hermitian K-theory.
Utilized the geometry of orthogonal and hyperbolic Grassmannians over the scheme S.
Examined candidates within the motivic stable homotopy category.
The constructed cellular absolute motivic spectrum aligns with the motivic ring spectrum reported in prior works.
Demonstrates a significant equivalence in theories of hermitian K-theory.

Abstract

Abstract In the Morel-Voevodsky motivic stable homotopy category of a quasi-compact quasi-separated scheme S , several candidates exist for a motivic spectrum representing hermitian K -theory. This note shows that the cellular absolute motivic spectrum constructed in 9 via the geometry of orthogonal and hyperbolic Grassmannians over S coincides with the motivic ring spectrum constructed in 4.

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