EXPLICIT FROBENIUS DESCENT FOR D+ - MODULES/

In his theory of D(X)dagger-modules, P. Berthelot has proved a general theorem of Frobenius descent. On the other hand, Christol and others have also proved various statements about weak Frobenius structures on an annulus of the rigid projective line. It is the aim of this paper to give some explicit and global formulas for Frobenius descent for D( X)dagger-modules. It requires us to build a new kind of differential o perator which represents Dwork's psi operator. The construction uses m ainly Taylor series properties. It is possible to derive from this som e new proofs of Christol's theorems; it is also useful for computation s in characteristic p like those arising in the construction of Cartie r's isomorphism or Cartier's operator. (C) 1998 Academic Press.