RESEARCH ANNOUNCEMENTS Dagger Formal Geometry and de Rham Cohomology

Let K be a finite extension of Q_p with R its ring of integers and k=F_q its residue field.Let π be a uniformizer of R. At first, let us recall some concepts. A K-linear map L:M→M is called nuclear, if the following two conditions hold. (ⅰ) For every λ≠0 in K~(ac) the algebraic closure of K with g the minimal polynomial of λ over K, ∪(Ker(g(L)~n)) is of finite dimension. (ⅱ) The nonzero eigenvalues of L, form a finite set or a sequence with a limit 0. Let us define

RESEARCH ANNOUNCEMENTS Dagger Formal Geometry and de Rham Cohomology