Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications
Jan Hendrik Bruinier, Benjamin Howard, Stephen S. Kudla, Michael Rapoport, Tonghai Yang
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.
Topics & Concepts
MathematicsUnitary stateModularity (biology)Shimura varietySeries (stratigraphy)ArithmeticAlgebra over a fieldPure mathematicsModular formGeneticsPolitical scienceBiologyPaleontologyLawAlgebraic Geometry and Number TheoryAdvanced Algebra and GeometryAnalytic Number Theory Research