  We formulate analogues, for Noetherian local $\mathbb Q$-algebras which are
not necessarily regular, of the injectivity part of Gersten's conjecture in
algebraic $K$-theory, and prove them in various cases. Our results suggest that
the algebraic $K$-theory of such a ring should be detected by combining the
algebraic $K$-theory of both its regular locus and the infinitesimal
thickenings of its singular locus.
