Isocrystals associated to Arithmetic Jet Spaces

The aim of the talk is to discuss the construction of an isocrystal associated to abelian schemes over p-adic fields using the arithmetic jet space theory. Isocrystals are objects in p-adic Hodge theory that lead to Galois representations. A well-known example of isocrystals coming from geometry are the ones obtained from the de Rham cohomology of the scheme. We will also talk about the interaction of our object with the first deRham cohomology of the abelian scheme. This is a joint work with Jim Borger.