How is the Ogus conjecture explicitly stated, which is a variant of the Hodge and the Tate conjectures for crystalline cohomology ?
How do we build its class map cycle map, and how do we formulate its Poincaré duality theorem ? In other words, how do we define the class cycle map that Ogus conjecture predicts its surjectivity, and for which field of coefficients should we establish this surjectivity ?
Thanks in advance for your help.