Integral crystalline cohomology over very ramified valuation rings

We explain how to set up an integral version ( as opposed to ) of Fontaine's comparison between crystalline and étale cohomology, over -adic fields with arbitrary ramification index. The main results then are that Fontaine's map respects integrality of Tate-cycles, and a construction of versal deformations of -divisible groups with Tate-cycles. An appendix deals with finite generation of crystalline cohomology.