De Martin Hils
(joint work with Ehud Hrushovski, Jinhe Ye and Tingxiang Zou) We prove Lang-Weil type bounds for the number of rational points of difference varieties over finite difference fields, in terms of the transformal dimension of the variety and assuming the existence of a smooth rational point. It follows that in (certain) non-principle ultraproducts of finite difference fields the course dimension of a quantifier free type equals its transformal tran-scendence degree. The proof uses a strong form of the Lang-Weil estimates and, as key ingredi-ent to obtain equidimensional Frobenius specializations, the recent work of Dor and Hrushovski on the non-standard Frobenius acting on an algebraically closed non-trivially valued field, in particular the pure stable embeddedness of the residue difference field in this context.
De Arthur Forey
De Sylvy Anscombe
De Raf Cluckers
De Pablo Cubides Kovacsics
De Lothar Sebastian Krapp
De Michal Szachniewicz
De Ya'acov Peterzil
De Mariana Vicaria
De Matthias Aschenbrenner
De Philip Dittmann
De Adele Padgett
De Dalia Terhesiu
