The very effective covers of KO and KGL over Dedekind schemes
@inproceedings{Bachmann2022TheVE, title={The very effective covers of KO and KGL over Dedekind schemes}, author={Tom Bachmann}, year={2022} }
We answer a question of Hoyois–Jelisiejew–Nardin–Yakerson regarding framed models of motivic connective K-theory spectra over Dedekind schemes. That is, we show that the framed suspension spectrum of the presheaf of groupoids of vector bundles (respectively non-degenerate symmetric bilinear bundles) is the effective cover of KGL (respectively very effective cover of KO). One consequence is that, over any scheme, we obtain a spectral sequence from Spitzweck’s motivic cohomology to homotopy…
References
SHOWING 1-10 OF 15 REFERENCES
Motivic twisted K-theory
- Mathematics
- 2010
This paper sets out basic properties of motivic twisted K-theory with respect to degree three motivic cohomology classes of weight one. Motivic twisted K-theory is defined in terms of such motivic…
Motivic infinite loop spaces
- MathematicsCambridge Journal of Mathematics
- 2021
We prove a recognition principle for motivic infinite P1-loop spaces over an infinite perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of…
The generalized slices of Hermitian K‐theory
- Mathematics
- 2016
We compute the generalized slices (as defined by Spitzweck–Østvær) of the motivic spectrum KO (representing Hermitian K ‐theory) in terms of motivic cohomology and (a version of) generalized motivic…
The localization theorem for framed motivic spaces
- MathematicsCompositio Mathematica
- 2021
We prove the analog of the Morel–Voevodsky localization theorem for framed motivic spaces. We deduce that framed motivic spectra are equivalent to motivic spectra over arbitrary schemes, and we give…
Hermitian K-theory via oriented Gorenstein algebras
- Mathematics
- 2021
We show that hermitian K-theory is universal among generalized motivic cohomology theories with transfers along finite Gorenstein morphisms with trivialized dualizing sheaf. As an application, we…
The K-Book: An Introduction to Algebraic K-Theory
- Mathematics
- 2013
Projective modules and vector bundles The Grothendieck group $K_0$ $K_1$ and $K_2$ of a ring Definitions of higher $K$-theory The fundamental theorems of higher $K$-theory The higher $K$-theory of…
η$\eta$ ‐Periodic motivic stable homotopy theory over Dedekind domains
- MathematicsJournal of Topology
- 2022
We construct well‐behaved extensions of the motivic spectra representing generalized motivic cohomology and connective Balmer–Witt K$K$ ‐theory (among others) to mixed characteristic Dedekind schemes…
The Hilbert scheme of infinite affine space and algebraic K-theory
- Mathematics
- 2020
We study the Hilbert scheme $\mathrm{Hilb}_d(\mathbb{A}^\infty)$ from an $\mathbb{A}^1$-homotopical viewpoint and obtain applications to algebraic K-theory. We show that the Hilbert scheme…
Norms in motivic homotopy theory
- MathematicsAstérisque
- 2021
If $f : S' \to S$ is a finite locally free morphism of schemes, we construct a symmetric monoidal "norm" functor $f_\otimes : \mathcal{H}_{\bullet}(S')\to \mathcal{H}_{\bullet}(S)$, where…