24 apr 2018 -- 11:30
Aula Tricerri, DiMaI, Firenze
Abstract.
The philosophy of Tannaka duality tells us that geometric objects can be faithfully reflected by their symmetric monoidal categories of (quasi-)coherent sheaves. In modern homotopy theory, analogies of this kind have been exploited to provide novel geometric perspectives on purely homotopical data. In this talk, I will discuss a basic instance of this analogy: a categorical Proj construction for an E-infinity algebra in a symmetric monoidal category. When specialised to the case of a category of modules over an ordinary ring, this construction recovers Serre's classification of quasi-coherent sheaves on a Proj in algebraic geometry. Meanwhile, applying it to the symmetric algebra on the circle in the category of pointed homotopy types recovers the theory of (symmetric) spectra.