Tom Bachmann | Eta-periodic motivic stable homotopy theory

Seminar on A1-topology, motives and K-theory, January 21, 2021
Tom Bachmann (LMU Munich)
Eta-periodic motivic stable homotopy theory

The eta-periodic motivic sphere over fields has attracted considerable interest in the past: Ananyevskiy–Levine–Panin have proved that its rationalization is Eilenberg–MacLane, and various authors have studied its homotopy groups over specific fields. In this talk I will explain recent results obtained in joint work with Mike Hopkins, in which we establish structural properties of the eta-periodic category, over in principle general bases (containing 1/2). In particular we compute over Z[1/2] the eta-periodic stable stems, as well as the eta-periodic algebraic SL-cobordism groups.