THE HOMOTOPY K-THEORY FOR NON-ARCHIMEDEAN BORNOLOGICAL ALGEBRAS

I will define non-Archimedean bivariant K-theory. This is the target of the universal functor on the category of complete, torsion free bornological Zp-algebras that satisfies homotopy invariance, stability and excision, and is a non-Archimedean analogue of Cuntz's kk-theory for locally convex algebras. Since analytic and (rationalised) periodic cyclic homology are also functors satisfying this property, the universal property yields bivariant Chern characters between bivariant K-theory and bivariant analytic cyclic homology. Finally, we show that when the first variable is the ground ring Zp, bivariant K-theory yields a version of Weibel's homotopy algebraic K-theory.