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Algebraic Cycles and values of Green's functions

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arxiv 2208.08325 v1 pith:A6YK5EUY submitted 2022-08-17 math.NT math.AG

classification math.NTmath.AG
keywords conjecturecyclescurvefieldfunctionsgreenvalueswork
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abstract

We construct indecomposable cycles in the motivic cohomology group $H^3_{{\mathcal M}}(A,{\mathbb Q}(2))$ where $A$ is an Abelian surface over a number field or the function field of a base. When $A$ is the self product of the universal elliptic curve over a modular curve, these cycles can be used to prove algebraicity results for values of higher Green's functions, similar to a conjecture of Gross, Kohnen and Zagier. We formulate a conjecture which relates our work with the recent work of Bruinier-Ehlen-Yang on the conjecture of Gross-Kohnen-Zagier.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A note on higher Green's functions

    math.AG 2025-09 conditional novelty 6.0 of 10

    The weight-4 Gross-Zagier conjecture is reduced to Beilinson-Hodge and proved cycle-theoretically for 18 (conjecturally 23) genus-zero K3 mirror families.

  2. Algebraic cycles and values of Green's functions -- Products of Elliptic Curves

    math.AG 2025-02 reject novelty 6.0 of 10

    The paper constructs infinite families of indecomposable motivic cycles on products of elliptic curves and conditionally links their regulators to algebraicity of higher Green's function values.

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