# Isotropy of quadratic spaces in finite and infinite dimension

### Karim Johannes Becher

### Detlev W. Hoffmann

## Abstract

In the late 1970s, Herbert Gross asked whether there exist fields admitting anisotropic quadratic spaces of arbitrarily large finite dimensions but none of infinite dimension. We construct examples of such fields and also discuss related problems in the theory of central simple algebras and in Milnor $K$-theory.

## Cite this article

Karim Johannes Becher, Detlev W. Hoffmann, Isotropy of quadratic spaces in finite and infinite dimension. Doc. Math. 12 (2007), pp. 473–504

DOI 10.4171/DM/231