  This paper studies "pro-excision" for the K-theory of one-dimensional
(usually semi-local) rings and its various applications. In particular, we
prove Geller's conjecture for equal characteristic rings over a perfect field
of finite characteristic, give the first results towards Geller's conjecture in
mixed characteristic, and we establish various finiteness results for the
K-groups of singularities (covering both orders in number fields and singular
curves over finite fields).
