Deligne's conjecture on the critical values of Hecke L-functions

Abstract: We give a proof of Deligne's conjecture for critical algebraic Hecke characters, which relates the special value of a Hecke L-function up to a rational factor with a certain period. This generalises a result of Blasius in the case where the Hecke character is defined over a CM-field. In our approach, we make use of the recently constructed Eisenstein--Kronecker classes of Kings--Sprang, which allow for a cohomological interpretation of the L-value when the field of definition is an arbitrary totally imaginary number field. The key insight is that these classes can be naturally regarded as de Rham classes of Blasius' reflex motive, which already played a key role in Blasius' proof.

number theory

Audience: researchers in the topic

London number theory seminar

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