Homological residue fields as comodules over coalgebras

Abstract

We explicitly present homological residue fields for tensor triangulated categories as categories of comodules in a number of examples across algebra, geometry, and topology. Our results indicate that, despite their abstract nature, they are very natural objects and encode tangent data at the corresponding point on the spectrum.

11 pages, minor updates, to appear in the proceedings of the Abel Symposium 2022, Triangulated categories in representation theory and beyond