The spectrum of units of $K$-theory
| Autor: | Carmeli, Shachar, Luecke, Kiran |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | It is well known that the $[0,1]$ and $[0,2]$ Postnikov truncations of the units of the topological $K$-theories $\glone KO$ and $\glone \KU$, respectively, are split, and that the splitting is provided by the ($\Z/2$-graded) line bundles. In this note we give a similar splitting for the units of algebraic $K$-theories $\glone K(\Z)$ and $\glone K(\F_\ell)$ for a prime $\ell$. We also give a complete calculation of the connective spectrum of strict units of these $K$-theory spectra. Comment: 26 pages |
| Databáze: | arXiv |
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