English

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.

Keywords

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

R2 v1 2026-06-24T06:51:44.402Z