$K$-Theory of Truncated Polynomials
Abstract
We study the algebraic -theory of rings of the form . We do this via trace methods and filtrations on topological Hochschild homology and related theories by quasisyntomic sheaves. We produce computations for a perfectoid ring in terms of the big Witt vectors of , for a smooth curve over a perfectoid ring in terms of the prismatic cohomology of , and for a complete mixed characteristic discrete valuation rings with perfect residue field in terms of the prismatic cohomology and Hodge-Tate divisor of .
Cite
@article{arxiv.2211.11110,
title = {$K$-Theory of Truncated Polynomials},
author = {Noah Riggenbach},
journal= {arXiv preprint arXiv:2211.11110},
year = {2023}
}
Comments
39 pages, fixed several typos, moved some of the more technical discussion in the introduction into a new section, rewrote and added several parts of [v1] to improve readability following a referee report, and added the ramified case of Theorem 1.13(now Theorem 1.6)