The localisation theorem for the K-theory of stable ∞-categories
- We provide a fairly self-contained account of the localisation and cofinality theorems for the algebraic K-theory of stable infity-categories. It is based on a general formula for the evaluation of an additive functor on a Verdier quotient closely following work of Waldhausen. We also include a new proof of the additivity theorem of K-theory, strongly inspired by Ranicki's algebraic Thom construction, a short proof of the universality theorem of Blumberg, Gepner and Tabuada, and a second proof of the cofinality theorem which is based on the universal property of K-theory.
| Author: | Fabian Hebestreit, Andrea Lachmann, Wolfgang SteimleGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1087004 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/108700 |
| ISSN: | 0308-2105OPAC |
| ISSN: | 1473-7124OPAC |
| Parent Title (English): | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
| Publisher: | Cambridge University Press (CUP) |
| Type: | Article |
| Language: | English |
| Date of first Publication: | 2023/07/20 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/10/26 |
| Tag: | General Mathematics |
| Volume: | 154 |
| Issue: | 6 |
| First Page: | 1749 |
| Last Page: | 1785 |
| DOI: | https://doi.org/10.1017/prm.2023.35 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Differentialgeometrie | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung |
