Class field theory, Hasse principles and Picard-Brauer duality for two-dimensional local rings
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917706339450880 |
|---|---|
| author | Suzuki, Takashi |
| author_facet | Suzuki, Takashi |
| contents | We draw concrete consequences from our arithmetic duality for two-dimensional local rings with perfect residue field. These consequences include class field theory, Hasse principles for coverings and $K_{2}$ and a duality between divisor class groups and Brauer groups. To obtain these, we analyze the ind-pro-algebraic group structures on arithmetic cohomology obtained earlier and prove some finiteness properties about them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_01396 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Class field theory, Hasse principles and Picard-Brauer duality for two-dimensional local rings Suzuki, Takashi Number Theory Algebraic Geometry 11G45 (Primary) 14F20, 19F05, 11S25 (Secondary) We draw concrete consequences from our arithmetic duality for two-dimensional local rings with perfect residue field. These consequences include class field theory, Hasse principles for coverings and $K_{2}$ and a duality between divisor class groups and Brauer groups. To obtain these, we analyze the ind-pro-algebraic group structures on arithmetic cohomology obtained earlier and prove some finiteness properties about them. |
| title | Class field theory, Hasse principles and Picard-Brauer duality for two-dimensional local rings |
| topic | Number Theory Algebraic Geometry 11G45 (Primary) 14F20, 19F05, 11S25 (Secondary) |
| url | https://arxiv.org/abs/2210.01396 |