# 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}
}
• Tom Bachmann
• Published 3 June 2020
• Mathematics
• Journal of Topology
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…
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