Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.06148 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929380308025344 |
|---|---|
| author | Kufner, Han-Ung |
| author_facet | Kufner, Han-Ung |
| contents | In this paper we give a proof of Deligne's conjecture on the critical values of $L$-functions for arbitrary algebraic Hecke characters. This extends a result of Blasius, which only works in the case of CM fields. The key new insight is that the Eisenstein-Kronecker classes of Kings-Sprang, which allow for a cohomological interpretation of the value $L(χ,0)$ for Hecke characters $χ$ of arbitrary totally imaginary fields, can be regarded as de Rham classes of Blasius' reflex motive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deligne's conjecture on the critical values of Hecke $L$-functions Kufner, Han-Ung Number Theory In this paper we give a proof of Deligne's conjecture on the critical values of $L$-functions for arbitrary algebraic Hecke characters. This extends a result of Blasius, which only works in the case of CM fields. The key new insight is that the Eisenstein-Kronecker classes of Kings-Sprang, which allow for a cohomological interpretation of the value $L(χ,0)$ for Hecke characters $χ$ of arbitrary totally imaginary fields, can be regarded as de Rham classes of Blasius' reflex motive. |
| title | Deligne's conjecture on the critical values of Hecke $L$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2406.06148 |