The Even Filtration

Abstract: The even filtration, introduced by Hahn-Raksit-Wilson, is a canonical filtration attached to a commutative ring spectrum which measures its failure to be even. Despite its simple definition, the even filtration recovers many arithmetically important constructions, such as the Adams-Novikov filtration of the sphere or the Bhatt-Morrow-Scholze filtration on topological Hochschild homology, showing that they are all invariants of the ring spectrum alone. I will describe a linear variant of the even filtration which is naturally defined on associative rings and can be effectively calculated through resolutions of modules, leading one to dream of prismatic cohomology of E_2-ring spectra.