DGAs with polynomial homology and $E_1$-quotients

Speaker: Julius Frank – University of Aberdeen

Abstract: Differential graded algebras whose homology is a graded polynomial algebra in one variable are surprisingly sparse. One example can be obtained by taking the derived $E_1$-quotient of a commutative ring by some prime $p$. This construction also shows up in some algebraic K-theory calculations, which motivates investigating this algebra with trace methods.

Examples are necessarily non-commutative: I will explain how all $E_2$-DGAs with polynomial homology over a fixed perfect ring are equivalent as ring spectra.