Finite quadratic modules and lattices
Number Theory
2023-08-31 v1
Abstract
We give a new proof of the fact that any finite quadratic module can be decomposed into indecomposable ones. For any indecomposable finite quadratic module, we construct a lattice, and a positive definite lattice, both of which are of the least rank, whose discriminant module is the given one. The resulting lattices are given by their Gram matrices explicitly.
Cite
@article{arxiv.2110.06783,
title = {Finite quadratic modules and lattices},
author = {Xiao-Jie Zhu},
journal= {arXiv preprint arXiv:2110.06783},
year = {2023}
}
Comments
33 pages