Topology Seminar Thursday 26 September, 13:15-14:15, 822 Møterom, Sentralbygg 2

Tasos Moulinos (Université Paris 13): The synthetic Hilbert additive group

Abstract: The Hilbert additive group scheme arises in algebraic geometry as the "unipotent completion" of the integers over Spec(Z). At the level of functions, it carries a canonical filtration compatible with the group structure. This is intimately related to the HKR filtration on Hochschild homology.

I will briefly review the above story and then discuss ongoing work (joint with Alice Hedenlund) on lifting the Hilbert additive group, together with its filtration on functions, to the setting of spectral algebraic geometry. This crucially uses the yoga of even filtrations, introduced by Hahn-Raksit-Wilson.