η-Periodic motivic stable homotopy theory over Dedekind domains

Bachmann, Tom (2022): η-Periodic motivic stable homotopy theory over Dedekind domains. In: Journal of Topology, Vol. 15, No. 2: pp. 950-971

Abstract

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 eta$\eta$-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 eta$\eta$-periodized algebraic symplectic and SL${\rm SL}$-cobordism groups of mixed characteristic Dedekind schemes containing 1/2$1/2$.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1753-8416
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892