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Main Author: Kufner, Han-Ung
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2406.06148
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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