2020
DOI: 10.2140/pjm.2020.309.71
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The arithmetic Hodge index theorem and rigidity of dynamical systems over function fields

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Cited by 1 publication
(10 citation statements)
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“…Faltings [17] and Hriljac [21] independently proved the same for arithmetic surfaces, by equating the arithmetic intersection product to the negative of the Néron-Tate height pairing on the Jacobian of the generic fiber, which was then generalized by Moriwaki [26] to higher dimensional arithmetic varieties. Here we extend the work of Yuan-Zhang [42] and the author [7] for adelic line bundles to arbitrary finitely generated fields.…”
Section: Introductionmentioning
confidence: 78%
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“…Faltings [17] and Hriljac [21] independently proved the same for arithmetic surfaces, by equating the arithmetic intersection product to the negative of the Néron-Tate height pairing on the Jacobian of the generic fiber, which was then generalized by Moriwaki [26] to higher dimensional arithmetic varieties. Here we extend the work of Yuan-Zhang [42] and the author [7] for adelic line bundles to arbitrary finitely generated fields.…”
Section: Introductionmentioning
confidence: 78%
“…Let X → B be a projective arithmetic model for X/K, and let L be a (Hermitian) line bundle on X with generic fiber L = L K . As described in [7,42], L induces a metric of L an , which in turn induces a model metric on L an . Thus we have a map…”
Section: 2mentioning
confidence: 99%
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