  We describe chromatic localisations of genuine L-spectra of discrete rings
and deduce that the purity property of $K(1)$-local $K$-theory of rings
established by Bhatt-Clausen-Mathew also holds in Grothendieck-Witt theory. In
addition, we collect some results on higher chromatic localisations of various
L-theory spectra and their consequences for Grothendieck-Witt theory.
