Abstract: We develop the theory of delta characters of Anderson modules. Given any Anderson module E, we construct a canonical z-isocrystal with a canonical Hodge-Pink structure. As an application, we show that when E is a Drinfeld module, our constructed z-isocrystal is weakly admissible given that a delta-parameter is non-zero. Therefore the equal characteristic analogue of the Fontaine functor associates a local shtuka and hence a crystalline z-adic Galois representation. It is also well known that there is a natural local shtuka attached to E. In the case of Carlitz modules, we show that our Galois representation is indeed the usual one coming from the Tate module. Hence this further raises the question of how the above two apparently different Galois representations compare with each other for a Drinfeld module of arbitrary rank. This is joint work with Sudip Pandit.

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