Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications
Copyright policy )Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications
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.
Final version. To appear in Asterisque
- Boston College United States
- UNIVERSITY OF WISCONSIN-MADISON United States
14G35, 11F55, 11F27, Mathematics - Algebraic Geometry, Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), Algebraic Geometry (math.AG)
14G35, 11F55, 11F27, Mathematics - Algebraic Geometry, Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), Algebraic Geometry (math.AG)
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