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
收藏
页码：1629 / 1693
页数：65
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