EXCEPTIONAL SPLITTING OF REDUCTIONS OF ABELIAN SURFACES

被引：8

作者：

Shankar, Ananth N. ^{[1
]}

Tang, Yunqing ^{[2
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

DUKE MATHEMATICAL JOURNAL | 2020年 / 169卷 / 03期

基金：

美国国家科学基金会;

关键词：

BORCHERDS PRODUCTS; VARIETIES; CURVES; MODELS; BOUNDS; FORMS;

D O I：

10.1215/00127094-2019-0046

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Heuristics based on the Sato-Tate conjecture and the Lang-Trotter philosophy suggest that an abelian surface defined over a number field has infinitely many places of split reduction. We prove this result for abelian surfaces with real multiplication. As in previous work by Charles and Elkies, this shows that a density 0 set of primes pertaining to the reduction of abelian varieties is infinite. The proof relies on the Arakelov intersection theory on Hilbert modular surfaces.

引用

页码：397 / 434

页数：38

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