The Fundamental Theorem of Localizing Invariants

Autor:	Saunier, Victor
Rok vydání:	2022
Předmět:	Mathematics - K-Theory and Homology Mathematics - Algebraic Topology Mathematics - Category Theory 18F25 19D55 19D50
Zdroj:	Ann. K-Th. 8 (2023) 609-643
Druh dokumentu:	Working Paper
DOI:	10.2140/akt.2023.8.609
Popis:	We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better for Karoubi-localizing functors, the Verdier-localizing invariants which are additionally invariant under idempotent completion. This general fundamental theorem specializes to new formulas in the context of non-connective K-theory, topological Hochschild homology and topological cyclic homology as well as connective K-theory of arbitrary ring spectra, and generalizes several known formulas for algebraic K-theory of spaces or connective K-theory of ordinary rings, schemes and $\mathbb{S}$-algebras. Comment: 25 pages, comments welcome; v2: small corrections and added more comparison to other works; v3: improvements after a referee report
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2209.05818 Zobrazit plný text záznamu View this record from Arxiv