• Corpus ID: 245837871

The very effective covers of KO and KGL over Dedekind schemes

  title={The very effective covers of KO and KGL over Dedekind schemes},
  author={Tom Bachmann},
We answer a question of Hoyois–Jelisiejew–Nardin–Yakerson regarding framed models of motivic connective K-theory spectra over Dedekind schemes. 1. Statement of results Let S be a scheme. The category PΣ(Cor (S)) of presheaves with framed transfers [5, §2.3] is a motivic analog of the classical category of E∞-monoids. We have the framed suspension spectrum functor Σ∞fr : PΣ(Cor (S))→ SH(S) which was constructed in [6, Theorem 18]. By analogy with the classical situation, one might expect that… 


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
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
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
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
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
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
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
The K-Book: An Introduction to Algebraic K-Theory
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
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