Simplicial Abel-Jacobi maps and reciprocity laws
classification
🧮 math.AG
keywords
lawsmapsreciprocitysatisfiedabel-jacobichowclarifyingcohomology
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We describe an explicit morphism of complexes that induces the cycle-class maps from (simplicially described) higher Chow groups to rational Deligne cohomology. The reciprocity laws satisfied by the currents we introduce for this purpose are shown to provide a clarifying perspective on functional equations satisfied by complex-valued di- and trilogarithms.
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