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Transactions of the American Mathematical Society

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Canonical heights for correspondences


Author: Patrick Ingram
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 37P30; Secondary 37F05
DOI: https://doi.org/10.1090/tran/7288
Published electronically: May 30, 2018
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Abstract: The canonical height associated to a polarized endomorphism of a projective variety, constructed by Call and Silverman and generalizing the Néron-Tate height on a polarized abelian variety, plays an important role in the arithmetic theory of dynamical systems. We generalize this construction to polarized correspondences, prove various fundamental properties, and show how the global canonical height decomposes as an integral of a local height over the space of absolute values on the algebraic closure of the field of definition.


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Additional Information

Patrick Ingram
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
Address at time of publication: York University, Toronto, Canada M3J1P3

DOI: https://doi.org/10.1090/tran/7288
Received by editor(s): June 7, 2015
Received by editor(s) in revised form: July 13, 2016, and March 29, 2017
Published electronically: May 30, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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