Overconvergent Witt vectors

Abstract

Let A be a finitely generated algebra over a field K of characteristic p > 0. We introduce a subring W †(A) ⊂W (A), which we call the ring of overconvergent Witt vectors and prove its basic properties. In a subsequent paper we use the results to define an overconvergent de Rham-Witt complex for smooth varieties over K whose hypercohomology is the rigid cohomology.