Description:
AbstractThis 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 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.