Arithmetic diagonal cycles on unitary Shimura varieties

Abstract

We define variants of PEL type of the Shimura varieties that appear in the context of the Arithmetic Gan-Gross-Prasad 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.

We removed all mention of an 'exotic level structure". Final version. To appear in Compositio Mathematica

References in corpus (2)

• Endoscopic Classification of Representations: Inner Forms of Unitary Groups
• On the arithmetic transfer conjecture for exotic smooth formal moduli spaces

Cited by in corpus (6)

• Kudla--Rapoport cycles and derivatives of local densities
• Fine Deligne-Lusztig varieties and Arithmetic Fundamental Lemmas
• On Shimura varieties for unitary groups
• On the Arithmetic Fundamental Lemma conjecture over a general $p$-adic field
• The Gross-Zagier-Zhang formula over function fields
• An arithmetic intersection conjecture