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Deligne's conjecture on the critical values of Hecke $L$-functions
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abstract
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 $L(\chi,0)$ for Hecke characters $\chi$ of arbitrary totally imaginary fields, can be regarded as de Rham classes of Blasius' reflex motive.
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Cited by 1 Pith paper
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Period relations for Rankin-Selberg convolutions for $\mathrm{GL}(n)\times\mathrm{GL}(n)$
Period relations for critical values of GL(n)xGL(n) Rankin-Selberg L-functions are proved over number fields containing a CM field.
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