Potential automorphy of certain non self-dual 3-dimensional Galois representations
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910436105912320 |
|---|---|
| author | Miagkov, Konstantin |
| author_facet | Miagkov, Konstantin |
| contents | In a series of papers, van Geemen and Top have defined a family of surfaces $S_z$ indexed by a nonzero integer parameter $z$, and a compatible family of 3-dimensional Galois representations over $\Q(i)$ attached to each surface. In this note we use recent advancements in potential automorphy and automorphy lifting to show that these compatible families are potentially automophic for all values of $z$, and hence that their L-functions have analytic continuation and a functional equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Potential automorphy of certain non self-dual 3-dimensional Galois representations Miagkov, Konstantin Number Theory 11F80 (Primary) 11F70 (Secondary) In a series of papers, van Geemen and Top have defined a family of surfaces $S_z$ indexed by a nonzero integer parameter $z$, and a compatible family of 3-dimensional Galois representations over $\Q(i)$ attached to each surface. In this note we use recent advancements in potential automorphy and automorphy lifting to show that these compatible families are potentially automophic for all values of $z$, and hence that their L-functions have analytic continuation and a functional equation. |
| title | Potential automorphy of certain non self-dual 3-dimensional Galois representations |
| topic | Number Theory 11F80 (Primary) 11F70 (Secondary) |
| url | https://arxiv.org/abs/2405.02970 |