论文标题
算术局部对称歧管的分析扭转和$ l^2 $ torsion的近似
Analytic torsion for arithmetic locally symmetric manifolds and approximation of $L^2$-torsion
论文作者
论文摘要
在本文中，我们为通过算术晶格定义了非阳性曲率对称空间的对称空间的分析扭转版本。该定义基于对相应热算子的重新归一化痕迹的研究，该痕迹定义为应用于热核的Arthur痕量公式的几何侧。然后，我们研究了分析扭转的限制行为，因为晶格通过固定算术亚组的一系列一致性亚组进行。我们的主要结果指出，对于主要一致性亚组的序列，在固定有限的位置和强范围的扁平捆绑包中收敛到1，分析扭转的对数，由子组的索引分开，收敛到$ l^2 $ nathalytic-Analytic Torsion。
In this paper we define a regularized version of the analytic torsion for quotients of a symmetric space of non-positive curvature by arithmetic lattices. The definition is based on the study of the renormalized trace of the corresponding heat operators, which is defined as the geometric side of the Arthur trace formula applied to the heat kernel. Then we study the limiting behavior of the analytic torsion as the lattices run through a sequence of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for sequences of principal congruence subgroups, which converge to 1 at a fixed finite set of places and strongly acyclic flat bundles, the logarithm of the analytic torsion, divided by the index of the subgroup, converges to the $L^2$-analytic torsion.
