Simplicial Abel-Jacobi maps and reciprocity laws
Algebraic Geometry
2015-08-06 v2
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.
Cite
@article{arxiv.1502.05459,
title = {Simplicial Abel-Jacobi maps and reciprocity laws},
author = {Jose Ignacio Burgos Gil and Matt Kerr and James D. Lewis and Patrick Lopatto},
journal= {arXiv preprint arXiv:1502.05459},
year = {2015}
}
Comments
51 pages, 1 figure; appendix by Burgos Gil added