  The first part of this paper introduces an analogue, for one-dimensional,
singular, complete local rings, of Gersten's injectivity conjecture for
discrete valuation rings. Our main theorem is the verification of this
conjecture when the ring is reduced and contains Q, using methods from
cyclic/Hochschild homology and Artin-Rees type results due to A. Krishna.
  The second part of the paper describes the relationship between adele type
resolutions of K-theory on a one-dimensional scheme and more classical
questions in K-theory such as localisation and descent. In particular, we
construct a new resolution of sheafified K-theory, conditionally upon the
conjecture.
