Abstract:
Following Chapter 6 of Hahn, Raksit, and Wilson’s paper on even filtrations, we equip THH(\ell) and THH(ku) with the motivic filtration and compute the associated graded of the motivic filtration on TC(\ell) and TC(ku). This provides a description of syntomic cohomology for connective K-theory and the Adams summand, yielding a computation of the homotopy groups of TC(ku) and TC(\ell) that differs from the one by Ausoni and Rognes.