Arithmetic diagonal cycles on unitary Shimura varieties
Michael Rapoport, Brian D. Smithling, W. Zhang
Abstract
We define variants of PEL type of the Shimura varieties that appear in the context of the arithmetic Gan–Gross–Prasad (AGGP) conjecture. We formulate for them a version of the AGGP conjecture. We also construct (global and semi-global) integral models of these Shimura varieties and formulate for them conjectures on arithmetic intersection numbers. We prove some of these conjectures in low dimension.
Topics & Concepts
MathematicsShimura varietyUnitary stateConjectureDimension (graph theory)DiagonalArithmeticIntersection (aeronautics)Context (archaeology)Pure mathematicsAlgebra over a fieldGeometryModular formLawBiologyPaleontologyAerospace engineeringPolitical scienceEngineeringAdvanced Algebra and GeometryAlgebraic Geometry and Number TheoryAnalytic Number Theory Research