In joint work with Michael Wibmer we discovered an equivalence of categories between etale difference algebras and certain profinite spaces with a continuous self-map.

Moreover, etale difference algebras of finite presentation correspond to subshifts of finite type (SFT) as studied in symbolic dynamics. We can thus make quick advances in difference algebra by exploiting the well-understood facts from symbolic dynamics. On the other hand, we hope that our difference algebraic-geometric point of view will contribute back to symbolic dynamics and the classification/decomposition of SFTs.

We will touch upon the theories of the etale fundamental group and etale cohomology of difference schemes, and discuss their relevance in this context.