Oisin Flynn-Connolly: Strictly commutative dg-algebras in positive characteristic

Abstract.

In this talk, we shall discuss the relationship between strictly commutative dg-algebras and E-infinity algebras in positive characteristic. In the first part, we work over \(\mathbb{F}_p\). We construct the secondary cohomology operations for a strictly commutative dg-algebra. We study the obstruction theories these induce, constructing several counterexamples. We shall see that an E-infinity algebra admits a commutative model iff its higher Steenrod operations vanish coherently. In the second part, we construct a de Rham-like complex over the p-adic numbers which provides a "best strictly commutative approximation" to the singular chains complex, and we study the question of its formality.