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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Cocycles on tropical varieties via piecewise polynomials
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by Georges Francois PDF
Proc. Amer. Math. Soc. 141 (2013), 481-497 Request permission


We use piecewise polynomials to define tropical cocycles generalising the well-known notion of tropical Cartier divisors to higher codimensions. Groups of cocycles are tropical analogues of Chow cohomology groups. We also introduce an intersection product of cocycles with tropical cycles (the counterpart of the classical cap product) and prove that this gives rise to a Poincaré duality in some cases.
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Additional Information
  • Georges Francois
  • Affiliation: Fachbereich Mathematik, Technische Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
  • Email:
  • Received by editor(s): March 29, 2011
  • Received by editor(s) in revised form: July 5, 2011
  • Published electronically: June 22, 2012
  • Additional Notes: The author is supported by the Fonds National de la Recherche (FNR), Luxembourg.
  • Communicated by: Lev Borisov
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 481-497
  • MSC (2010): Primary 14T05; Secondary 14C17, 14F99
  • DOI:
  • MathSciNet review: 2996952