D-dagger(infinity)-affinity of projective schemes.

Let V be a discrete, complete, valuation ring of unequal characteristics (0 ,p), and X a formal projective smooth scheme on the formal spectrum of V. L et Z be an ample divisor on X, and U the affine open set which is the compl ement of Z into X. In this situation, Berthelot constructed the sheaf of ar ithmetic differential operators with overconvergent coefficients along Z, d enoted by D dagger(co). We prove here that X is D dagger(infinity)-affine. This result corroborates the idea that the category of coherent D dagger(in finity)-modules can be viewed as attached to the affine open set U.