Adrian Iovita

Crystalline comparison isomorphisms for formal schemes

Given a smooth proper scheme over the ring of integers of a p-adic field, the crystalline comparison isomorphisms relate the \'etale cohomology groups of the geometric generic fiber of our scheme to the respective crystalline cohomology groups of its special fiber, after base change to the ring of periods Bcris. Faltings proved the existence of these isomorphisms in 1989. Together with F. Andreatta we have a new way of approaching this problem which allows to an extension of the result to smooth formal schemes.