Abstract Goerss-Hopkins theory

2019/04/18 by Pstrągowski, Piotr, VanKoughnett, Paul · 2 citations
#55P43 (Secondary) #55S35 (Primary) 55P42 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.08881

Abstract

We present an abstract version of Goerss-Hopkins theory in the setting of a prestable ∞-category equipped with a suitable periodicity operator. In the case of the ∞-category of synthetic spectra, this yields obstructions to realizing a comodule algebra as a homology of a commutative ring spectrum, recovering the results of Goerss and Hopkins.

Cited by

• A rigidity theorem for π_*-étale \mathbb E_k-algebras
• Spectral moduli problems for level structures and an integral Jacquet-Langlands dual of Morava E-theory

Related

• Goerss--Hopkins obstruction theory for ∞-categories
• Hermitian K-theory for stable ∞-categories II: Cobordism categories and additivity
• An Introduction to Higher Categorical Algebra
• Synthetic spectra and the cellular motivic category
• On Bialgebras, Comodules, Descent Data and Thom Spectra in ∞-categories