# E-infinity projective geometry and symmetric spectra

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Andrew Macpherson

created by daniele on 11 Apr 2018

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.