Canonical heights for correspondences

Ingram, Patrick

doi:10.1090/tran/7288

Canonical heights for correspondences
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Trans. Amer. Math. Soc. 371 (2019), 1003-1027 Request permission

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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