Speaker: Scott Balchin (University of Warwick)
Title: Adelic reconstruction in prismatic homotopy theory
Abstract: Prismatic homotopy theory is the study of stable monoidal homotopy theories through their Balmer spectrum. In this talk, I will discuss how one can use localised p-complete data at each Balmer prime in an adelic fashion to reconstruct the homotopy theory in question. There are two such models, one is done by moving to categories of modules, which, for example, recovers the algebraic models for G-equivariant cohomology theories of Greenlees-Shipley. The other, newer model, works purely at the categorical level and requires the theory of weighted homotopy limits.
This is joint work with J.P.C Greenlees.