Add to ORKGIn this article, under a certain hypothesis on equivariant Hodge theory, we construct the Hodge realization of the polylogarithm class in the equivariant Deligne-Beilinson cohomology of a certain algebraic torus associated to a totally real field. We then prove that the de Rham realization of this polylogarithm gives the Shintani generating class, a cohomology class generating the values of the Lerch zeta functions of the totally real field at nonpositive integers. Inspired by this result, we give a conjecture concerning the specialization of this polylogarithm class at torsion points, and discuss its relation to the Beilinson conjecture for Hecke characters of totally real fields.Comment: 52 page
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In this article, we construct the Hodge realization of the polylogarithm class in the equivariant De...
In 2014, Kings and Rossler showed that the realization of the degree zero part of the abelian polylo...
To any element of a connected, simply connected, semisimple complex algebraic group G and a choice o...
Let $K$ be a mixed characteristic complete discrete valuation field with perfect residue field, and ...
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The solution of Shareshian-Wachs conjecture by Brosnan-Chow linked together the cohomology of regula...
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