Simplicial Abel-Jacobi maps and reciprocity laws

Matt Kerr; James Lewis; Patrick Lopatto; José Ignacio Burgos-Gil

doi:10.1090/jag/692

Simplicial Abel-Jacobi maps and reciprocity laws

Matt Kerr
, James Lewis
, Patrick Lopatto
, José Ignacio Burgos-Gil

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Pages (from-to)	121-172
Number of pages	52
Journal	Journal of Algebraic Geometry
Volume	27
Issue number	1
DOIs	https://doi.org/10.1090/jag/692
State	Published - 2018

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title = "Simplicial Abel-Jacobi maps and reciprocity laws",

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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AU - Lopatto, Patrick

AU - Burgos-Gil, José Ignacio

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85035309154

U2 - 10.1090/jag/692

DO - 10.1090/jag/692

M3 - Article

AN - SCOPUS:85035309154

SN - 1056-3911

VL - 27

SP - 121

EP - 172

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

IS - 1

ER -

Simplicial Abel-Jacobi maps and reciprocity laws

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