Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Simplicial Abel-Jacobi maps and reciprocity laws


Authors: Matt Kerr, James Lewis and Patrick Lopatto; With an Appendix by José Ignacio Burgos-Gil
Journal: J. Algebraic Geom. 27 (2018), 121-172
DOI: https://doi.org/10.1090/jag/692
Published electronically: July 21, 2017
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Abstract | References | Additional Information

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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Additional Information

Matt Kerr
Affiliation: Department of Mathematics, Campus Box 1146, Washington University in St. Louis, St. Louis, Missouri 63130
Email: matkerr@math.wustl.edu

James Lewis
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Email: lewisjd@ualberta.ca

Patrick Lopatto
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email: patricklopatto@gmail.com

José Ignacio Burgos-Gil
Affiliation: Instituto de Ciencias Matemáticas (CSIC-UAM-UCM-UCM3), Calle Nicolás Cabrera 15, Campus UAB, Cantoblanco, 28049 Madrid, Spain
Email: burgos@icmat.es

DOI: https://doi.org/10.1090/jag/692
Received by editor(s): November 25, 2015
Received by editor(s) in revised form: May 2, 2016
Published electronically: July 21, 2017
Article copyright: © Copyright 2017 University Press, Inc.

American Mathematical Society