Invariants and discriminant ideals of orthogonal complements in a quadratic space

2011/12/12 by Manabu Murata, Murata, Manabu · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1112.2454

openalex publication_date 2011/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies two topics concerning on the orthogonal complement of one dimensional subspace with respect to a given quadratic form on a vector space over a number field. One is to determine the invariants for the isomorphism class of such a complement in the sense of Shimura. The other is to investigate an ideal of the base field, which may be viewed as a difference between the genus of maximal lattices and an integral lattice in the complement. We shall discuss about the class number of the genus of maximal lattices as an application.

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