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Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications

Jan Hendrik Bruinier, Benjamin Howard, Stephen S. Kudla, Michael A. Rapoport, Tonghai Yang

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Abstract

We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings heights of abelian varieties with complex multiplication. These results are derived from the authors' earlier results on the modularity of generating series of divisors on unitary Shimura varieties.

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What this paper is about

We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings heights of abelian varieties with complex multiplication. These results are derived from the authors' earlier results on the modularity of generating series of divisors on unitary Shimura varieties.

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OpenAlex reports 13 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings heights of abelian varieties with complex multiplication. These results are derived from the authors' earlier results on the modularity of generating series of divisors on unitary Shimura varieties.

Key concepts: Mathematics, Unitary state, Modularity (biology), Shimura variety, Series (stratigraphy), Arithmetic, Algebra over a field, Pure mathematics

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