Deligne's conjecture on the critical values of Hecke $L$-functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929380308025344 |
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| 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 |