Thomason filtration via $T(1)$-local $\mathrm{TC}$
Abstract
We construct a natural filtration on -local for any animated commutative rings using prismatic cohomology and descent theory. In the course of the construction, we also study some general properties of prismatic cohomology complexes over perfect prisms after inverting distinguished generators. The construction is intrinsic to and recovers Thomason's spectral sequence for -local algebraic K-theory via the cyclotomic trace map; as a consequence, we also recover the \'etale comparison for prismatic cohomology.
Cite
@article{arxiv.2305.07576,
title = {Thomason filtration via $T(1)$-local $\mathrm{TC}$},
author = {Hyungseop Kim},
journal= {arXiv preprint arXiv:2305.07576},
year = {2025}
}
Comments
v3: accepted version, 40 pages; v2: Major updates including new constructions and extensions to all animated commutative rings. Added comparison with the \'etale Postnikov filtration from algebraic K-theory side and a consequent \'etale comparison