---
res:
bibo_abstract:
- Suppose Q is a definite quadratic form on a vector space V over some totally real
field K ≠ Q. Then the maximal integral Zₖ-lattices in (V,Q) are locally isometric
everywhere and hence form a single genus. We enumerate all orthogonal spaces (V,Q)
of dimension at least 3, where the corresponding genus of maximal integral lattices
consists of a single isometry class. It turns out, there are 471 such genera.
Moreover, the dimension of V and the degree of K are bounded by 6 and 5 respectively.
This classification also yields all maximal quaternion orders of type number one.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Markus
foaf_name: Kirschmer, Markus
foaf_surname: Kirschmer
foaf_workInfoHomepage: http://www.librecat.org/personId=82258
bibo_doi: 10.1016/j.jnt.2013.10.007
bibo_volume: 136
dct_date: 2014^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0022-314X
dct_language: eng
dct_publisher: Elsevier BV@
dct_subject:
- Algebra and Number Theory
dct_title: One-class genera of maximal integral quadratic forms@
...