• Corpus ID: 245837871

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
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
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
η$\eta$ ‐Periodic motivic stable homotopy theory over Dedekind domains
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 generalized slices of Hermitian K‐theory
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
On very effective hermitian K-theory
We argue that the very effective cover of hermitian K-theory in the sense of motivic homotopy theory is a convenient algebro-geometric generalization of the connective real topological K-theory
The localization theorem for framed motivic spaces
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
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
Lecture Notes On Motivic Cohomology
* Etale motivic theory: * Etale sheaves with transfers * The relative Picard group and Suslin's rigidity theorem * Derived tensor products $\mathbb{A}^1$-weak equivalence * Etale motivic cohomology
Norms in motivic homotopy theory
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
...
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