# Separable extensions of orthogonal involutions in characteristic two

## TL;DR

This paper proves that anisotropic orthogonal involutions in characteristic two are totally decomposable if they become so over a separable extension, confirming a conjecture in this setting.

## Contribution

It establishes a characteristic two analogue of a conjecture by Bayer-Fluckiger et al. regarding involutions and their decomposability over separable extensions.

## Key findings

- Anisotropic orthogonal involutions are totally decomposable over the base field if they are over a separable extension.
- The result confirms a conjecture for characteristic two fields.
- Provides a key step in understanding involutions in characteristic two.

## Abstract

It is shown that an anisotropic orthogonal involution in characteristic two is totally decomposable if it is totally decomposable over a separable extension of the ground field. In particular, this settles a characteristic two analogue of a conjecture formulated by Bayer-Fluckiger et al.