Cycles d'ordre au moins 16 dans le 2-groupe des classes d'idéaux de certains corps quadratiques
We find all possible cycle-lengths for polynomial mappings in two variables over rings of integers in quadratic extensions of rationals.
Several interesting lattices can be realised as ideal lattices over cyclotomic fields : some of the root lattices, the Coxeter-Todd lattice, the Leech lattice, etc. Many of these are modular in the sense of Quebbemann. The aim of the present paper is to determine the cyclotomic fields over which there exists a modular ideal lattice. We then study an especially simple class of lattices, the ideal lattices of trace type. The paper gives a complete list of modular ideal lattices of trace type defined...