Affiliation:
1. École Polytechnique Fédérale de Lausanne, Institut de Mathãl'matiques Bernoulli, CH-1015 Lausanne, Switzerland
Abstract
We study some properties of Arakelov-modular lattices, which are particular modular ideal lattices over CM fields. There are two main results in this paper. The first one is the determination of the number of Arakelov-modular lattices of fixed level over a given CM field provided that an Arakelov-modular lattice is already known. This number depends on the class numbers of the CM field and its maximal totally real subfield. The first part gives also a way to compute all these Arakelov-modular lattices. In the second part, we describe the levels that can occur for some multiquadratic CM number fields.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory