ANALYTIC CYCLIC HOMOLOGY IN POSITIVE CHARACTERISTIC

We define a homology theory for complete torsion-free bornological algebras over a complete discrete valuation ring. The theory satisfies homotopy invariance, Morita invariance and excision. We use these properties to compute our theory for Leavitt path algebras. For coordinate rings of smooth curves, our theory agrees with Berthelot's rigid cohomology. Furthermore, using the theory for torsion-free algebras, we construct a homology theory for algebras over finite fields by lifting such algebras to complete torsion-free algebras over the p-adic integers. The main result shows that the theory we define is independent of the choices of liftings to torsion-free algebras. This project is joint work with Guillermo Cortiñas and Ralf Meyer.