  Let V be a complete discrete valuation ring with uniformiser p. We introduce
an invariant of Banach V-algebras called local cyclic homology. This invariant
is related to analytic cyclic homology for complete, bornologically torsionfree
V-algebras. It is shown that local cyclic homology only depends on the
reduction mod p of a Banach V-algebra and that it is homotopy invariant,
matricially stable, and excisive.
