Generalized crystalline cohomology theories

For a prime number p, the crystalline cohomology of an F_p-scheme can be regarded as an analogue of the singular cohomology with Z_p coefficients of a topological space. On the topological side, there are other “generalized” cohomology theories, e.g. K-theory and cobordism, and these are related to natural operations on singular cohomology. In this talk, I will discuss analogues of these generalized cohomology theories and cohomology operations in the crystalline setting.