### Rationally isotropic quadratic spaces are locally isotropic, by Ivan Panin

In this preprint we consider a regular local ring, a quadratic space
over the ring and a unit. Assuming that the ring contains the rational
number field we prove the following result. If the space represents
the unit over the quotient field of the ring then the space represents
the unit over the ring too. The proof is based on a variant of the
Springer theorem and on a moving lemma. The variant of the Springer
theorem is proved in a joint work with U. Rehmann. The moving lemma
is inspired by a moving lemma for algebraic cobordism proved by
M. Levine and F. Morel.

Ivan Panin <panin@pdmi.ras.ru>