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arXiv · 1502.05459

Simplicial Abel-Jacobi maps and reciprocity laws

Jose Ignacio Burgos Gil·Matt Kerr·James D. Lewis·Patrick Lopatto
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Abstract

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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Jose Ignacio Burgos Gil, Matt Kerr, James D. Lewis, Patrick Lopatto. 2015-02-19. Simplicial Abel-Jacobi maps and reciprocity laws. https://arxiv.org/abs/1502.05459

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