Model theory of difference fields with an additive character on the fixed field

Stefan Marian Ludwig

Paper

Model theory of difference fields with an additive character on the fixed field

Abstract

Following a research line proposed by Hrushovski in his work on pseudofinite fields with an additive character, we investigate the theory

which is the model companion of the theory of difference fields with an additive character on the fixed field added as a continuous logic predicate.

is the common theory (in characteristic

) of the algebraic closure of finite fields with the Frobenius automorphism and the standard character on the fixed field and turns out to be a simple theory. We fully characterise 3-amalgamation and deduce that the connected component of the Kim-Pillay group (for any completion of

) is abelian as conjectured by Hrushovski. Finally, we describe a natural expansion of

in which geometric elimination of continuous logic imaginaries holds.