The unipotent Albanese map and Selmer varieties for curves
We study the unipotent Albanese map that associates the torsor of paths for p-adic fundamental groups to a point on a hyperbolic curve. It is shown that the map is very transcendental in nature, while standard conjectures about the structure of mixed motives provide control over the image of the map...
| Main Author: | |
|---|---|
| Format: | Journal article |
| Published: |
Research Institute for Mathematical Sciences, Kyoto University
2009
|
| _version_ | 1826262315417206784 |
|---|---|
| author | Kim, M |
| author_facet | Kim, M |
| author_sort | Kim, M |
| collection | OXFORD |
| description | We study the unipotent Albanese map that associates the torsor of paths for p-adic fundamental groups to a point on a hyperbolic curve. It is shown that the map is very transcendental in nature, while standard conjectures about the structure of mixed motives provide control over the image of the map. As a consequence, conjectures of ‘Birch and Swinnerton-Dyer type’ are connected to finiteness theorems of Faltings-Siegel type. |
| first_indexed | 2024-03-06T19:34:29Z |
| format | Journal article |
| id | oxford-uuid:1e92fae4-0ab9-4e74-aac8-70f4a78a4b7b |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:34:29Z |
| publishDate | 2009 |
| publisher | Research Institute for Mathematical Sciences, Kyoto University |
| record_format | dspace |
| spelling | oxford-uuid:1e92fae4-0ab9-4e74-aac8-70f4a78a4b7b2022-03-26T11:17:05ZThe unipotent Albanese map and Selmer varieties for curvesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1e92fae4-0ab9-4e74-aac8-70f4a78a4b7bSymplectic Elements at OxfordResearch Institute for Mathematical Sciences, Kyoto University2009Kim, MWe study the unipotent Albanese map that associates the torsor of paths for p-adic fundamental groups to a point on a hyperbolic curve. It is shown that the map is very transcendental in nature, while standard conjectures about the structure of mixed motives provide control over the image of the map. As a consequence, conjectures of ‘Birch and Swinnerton-Dyer type’ are connected to finiteness theorems of Faltings-Siegel type. |
| spellingShingle | Kim, M The unipotent Albanese map and Selmer varieties for curves |
| title | The unipotent Albanese map and Selmer varieties for curves |
| title_full | The unipotent Albanese map and Selmer varieties for curves |
| title_fullStr | The unipotent Albanese map and Selmer varieties for curves |
| title_full_unstemmed | The unipotent Albanese map and Selmer varieties for curves |
| title_short | The unipotent Albanese map and Selmer varieties for curves |
| title_sort | unipotent albanese map and selmer varieties for curves |
| work_keys_str_mv | AT kimm theunipotentalbanesemapandselmervarietiesforcurves AT kimm unipotentalbanesemapandselmervarietiesforcurves |