# η$\eta$ ‐Periodic motivic stable homotopy theory over Dedekind domains

@article{Bachmann2022etaM, title={$\eta$\$\eta\$ ‐Periodic motivic stable homotopy theory over Dedekind domains}, author={Tom Bachmann}, journal={Journal of Topology}, year={2022}, volume={15} }

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 on which 2 is invertible. As a consequence, we lift the fundamental fiber sequence of η$\eta$ ‐periodic motivic stable homotopy theory established in Bachmann and Hopkins (2020) from fields to arbitrary base schemes, and use this to determine (among other things) the η$\eta$ ‐periodized algebraic…

## 7 Citations

### The Dual Motivic Witt Cohomology Steenrod Algebra

- Mathematics
- 2021

In this paper we begin the study of the (dual) Steenrod algebra of the motivic Witt cohomology spectrum HWZ by determining the algebra structure of HWZ∗∗HWZ over fields k of characteristic not 2…

### 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…

### Topological models for stable motivic invariants of regular number rings

- MathematicsForum of Mathematics, Sigma
- 2022

Abstract For an infinity of number rings we express stable motivic invariants in terms of topological data determined by the complex numbers, the real numbers and finite fields. We use this to extend…

### EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2021

We equate various Euler classes of algebraic vector bundles, including those of [12] and one suggested by M. J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler…

### The very effective covers of KO and KGL over Dedekind schemes

- Mathematics
- 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…

### $v_1$-periodic motivic homotopy over prime fields

- Mathematics
- 2022

. We compute the motivic stable homotopy groups of a variant of the connective image-of- J spectrum over prime ﬁelds of characteristic not two. Together with the analogous computation over…

### Punctured tubular neighborhoods and stable homotopy at infinity

- Mathematics
- 2022

We initiate a study of punctured tubular neighborhoods and homotopy theory at infinity in motivic settings. We use the six functors formalism to give an intrinsic definition of the stable motivic…

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