Bloch Groups of Rings
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911435593875456 |
|---|---|
| author | Coronado, Rodrigo Cuitun Hutchinson, Kevin |
| author_facet | Coronado, Rodrigo Cuitun Hutchinson, Kevin |
| contents | We give a definition of (refined) Bloch groups of general commutative rings which agrees with the standard definition in the case of local rings whose residue field has at least $4$ elements. Under appropriate conditions on a ring $A$, satisfied by any field or local ring, these groups are closely related to third homology of $\mathrm{SL}_2(A)$ and to indecomposable $K_3$ of $A$. We analyze these conditions. We calculate the Bloch groups of $\mathbb{F}_2,\mathbb{F}_3,\mathbb{Z}$ and $\mathbb{Z}[\frac{1}{2}]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_04996 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bloch Groups of Rings Coronado, Rodrigo Cuitun Hutchinson, Kevin K-Theory and Homology 20J06 We give a definition of (refined) Bloch groups of general commutative rings which agrees with the standard definition in the case of local rings whose residue field has at least $4$ elements. Under appropriate conditions on a ring $A$, satisfied by any field or local ring, these groups are closely related to third homology of $\mathrm{SL}_2(A)$ and to indecomposable $K_3$ of $A$. We analyze these conditions. We calculate the Bloch groups of $\mathbb{F}_2,\mathbb{F}_3,\mathbb{Z}$ and $\mathbb{Z}[\frac{1}{2}]$. |
| title | Bloch Groups of Rings |
| topic | K-Theory and Homology 20J06 |
| url | https://arxiv.org/abs/2201.04996 |