  Let A be a finitely generated algebra over a field K of characteristic p >0.
We introduce a subring of the ring of Witt vectors W(A). We call it the ring of
overconvergent Witt vectors. We prove that on a scheme X of finite type over K
the overconvergent Witt vectors are an \'etale sheaf. In a forthcoming paper
(Annales ENS) we define an overconvergent de Rham-Witt complex on a smooth
scheme X over a perfect field K whose hypercohomology is the rigid cohomology
of X in the sense of Berthelot.
