Deformation theory of $E_∞$-coalgebras and Mandell's theorem

Speaker: Florian Riedel – University of Copenhagen

Abstract: I discuss how we can use deformation theoretic methods to show that Weil-restriction of coalgebras lets us recover the $p$-completed suspension spectrum of a space from its $\mathbb{F}_ p$-homology as its unique lift to an $\mathbb{E}_\infty$-coalgebra in $p$-complete spectra. I will talk about higher deformation theory as developed by Lurie and introduce the notion of formally étale coalgebra. I will also sketch how this relates to work in progress on construct an integral coalgebraic model for the category of spaces.