Difference fields and descent of difference varieties
In this talk I will state and explain a few results of descent of difference varieties which can be obtained using model theoretic tools.
The typical statement is the following: Let K_1 and K_2 be difference fields, and V_i, i=1,2, difference varieties defined over K_i. Assume that there is a dominant rational difference morphism from V_1 onto V_2.
Then V_2 in turns dominates some difference variety defined over K=K_1\cap K_2. This result is of course not true as stated, and we explain which hypotheses make it valid. In particular it gives an alternate proof of a result of M. Baker on algebraic dynamics and generalises it to higher dimensions. This is joint work with Ehud Hrushovski.
Extended abstract, at http://www.logique.jussieu.fr/~zoe/papiers/Leeds09.pdf