The topological Hochschild homology of a commutative –algebra ( ring spectrum) naturally has the structure of a commutative –algebra in the strict sense, and of a Hopf algebra over in the homotopy category. We show, under a flatness assumption, that this makes the Bökstedt spectral sequence converging to the mod homology of into a Hopf algebra spectral sequence. We then apply this additional structure to the study of some interesting examples, including the commutative –algebras , , , and , and to calculate the homotopy groups of and after smashing with suitable finite complexes. This is part of a program to make systematic computations of the algebraic –theory of –algebras, by means of the cyclotomic trace map to topological cyclic homology.
"Hopf algebra structure on topological Hochschild homology." Algebr. Geom. Topol. 5 (3) 1223 - 1290, 2005. https://doi.org/10.2140/agt.2005.5.1223