# Isometries of quadratic spaces

### Eva Bayer-Fluckiger

EFPL, Lausanne, Switzerland

## Abstract

Let $k$ be a global field of characteristic not 2, and let $f \in k[X]$ be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial $f$ if and only if such an isometry exists over all the completions of $k$. This gives a partial answer to a question of Milnor.

## Cite this article

Eva Bayer-Fluckiger, Isometries of quadratic spaces. J. Eur. Math. Soc. 17 (2015), no. 7, pp. 1629–1656

DOI 10.4171/JEMS/541