TORSION HOMOLOGY GROWTH AND CYCLE COMPLEXITY OF ARITHMETIC MANIFOLDS

被引：24

作者：

Bergeron, Nicolas ^{[1
]}

Sengun, Mehmet Haluk ^{[2
]}

Venkatesh, Akshay ^{[3
]}

机构：

[1] Univ Paris 06, CNRS, UMR 7586, Inst Math Jussieu, Paris, France

[2] Univ Sheffield, Sch Math & Stat, Sheffield, S Yorkshire, England

[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

DUKE MATHEMATICAL JOURNAL | 2016年 / 165卷 / 09期

基金：

美国国家科学基金会;

关键词：

ELLIPTIC-CURVES; ANALYTIC TORSION; MULTIPLICITY ONE; REPRESENTATIONS; FORMS; NUMBER; BOUNDS; COEFFICIENTS; VARIETIES; SPECTRUM;

D O I：

10.1215/00127094-3450429

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be an arithmetic hyperbolic 3-manifold, such as a Bianchi manifold. We conjecture that there is a basis for the second homology of M, where each basis element is represented by a surface of "low" genus, and we give evidence for this. We explain the relationship between this conjecture and the study of torsion homology growth.

引用

页码：1629 / 1693

页数：65

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