A new approach to classification of integral quadratic forms over dyadic local fields

TL;DR

This paper introduces a simplified classification method for integral quadratic forms over dyadic local fields using BONGs, facilitating future research on quadratic form representation.

Contribution

It translates O'Meara's classification theorem into BONGs, providing a more straightforward approach as a foundation for solving representation problems.

Findings

Simplified classification of quadratic forms using BONGs

Established a basis for future representation problem solutions

Enhanced understanding of quadratic lattice descriptions

Abstract

We translate O'Meara's classification Theorem 93:28 in terms of BONGs. BONGs, short for "basis of norm generators", are a new way of describing quadratic lattices, an alternative to the traditional Jordan decompositions. They were introduced in [B]. Our result has its own merits as it is somewhat simpler than O'Meara's 93:28. However, it's main importance is that it is a prerequisite for a future work where we solve the more complicated problem of representation. [B] C. N. Beli, Integral spinor norms over dyadic local fields, J. Number Theory 102 (2003) 125-182.