Bonn Topology Group - Abstracts

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Talk

Akhil Mathew (Harvard University, Cambridge, USA): Nonconnective simplicial commutative rings
May 23rd, 2017

Abstract

Simplicial commutative rings are one of the first steps into "derived" rings that one can take. Many constructions for general E_\infty-ring spectra or even Z-algebras are simpler in the world of simplicial commutative rings; however, from a purely homotopy-theoretic or categorical picture they are slightly mysterious. I will explain ongoing work with Bhargav Bhatt on an extended theory of "generalized rings" which extends this category to allow nonconnective objects. Many "equational" constructions which cannot work with E_\infty-rings extend well to generalized rings.

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