2017/02/25 by Chao Li, Yihang Zhu
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry and Number Theory #Conjecture #Diagonal #Intersection (aeronautics) #Intersection number #Lemma (botany) #math.AG #math.NT #msc:11G18 #msc:14G17 #msc:22E55
paper · pdf · doi:10.1112/s0010437x18007108
published as Compositio Math. 154 (2018) 1407-1440 · Comments welcome
arxiv created 2017/02/25 · openalex created_date 2017/03/16 · openalex publication_date 2018/05/15 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/05
We prove an explicit formula for the arithmetic intersection number of diagonal cycles on GSpin Rapoport–Zink spaces in the minuscule case. This is a local problem arising from the arithmetic Gan–Gross–Prasad conjecture for orthogonal Shimura varieties. Our formula can be viewed as an orthogonal counterpart of the arithmetic–geometric side of the arithmetic fundamental lemma proved by Rapoport–Terstiege–Zhang in the minuscule case.