Arithmetic diagonal cycles on unitary Shimura varieties

被引：19

作者：

Rapoport, M. ^{[1
,2
]}

Smithling, B. ^{[2
]}

Zhang, W. ^{[3
]}

机构：

[1] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[3] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

来源：

COMPOSITIO MATHEMATICA | 2020年 / 156卷 / 09期

基金：

美国国家科学基金会;

关键词：

arithmetic Gan– Gross– Prasad conjecture; unitary Shimura varieties; arithmetic diagonal cycles; relative trace formula; Zagier formula; special values of L-functions; COMPLEX MULTIPLICATION CYCLES; HEIGHT PAIRINGS; REDUCTION; MODELS; JACQUET;

D O I：

10.1112/S0010437X20007289

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1745 / 1824

页数：81

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