# Similarity of quadratic forms over global fields in characteristic 2

## TL;DR

This paper proves that two non-degenerate quadratic forms over a global function field of characteristic 2 are similar over the entire field if they are similar over all completions, extending known results to characteristic 2.

## Contribution

It establishes an analogue of Ono's result for characteristic not 2, specifically for global function fields of characteristic 2.

## Key findings

- Quadratic forms similar over all local completions are similar globally.
- Extends classical local-global principles to characteristic 2.
- Provides new insights into quadratic form theory in characteristic 2.

## Abstract

Let $ K $ be a global function field of characteristic $ 2 $. For each non-trivial place $ v $ of $ K $, let $ K_{v} $ be the completion of $ K $ at $ v $. We show that if two non-degenerate quadratic forms are similar over every $ K_{v} $, then they are similar over $ K $. This provides an analogue of the version for characteristic not $ 2 $ previously obtained by T.Ono.