Linearization in ultrametric dynamics in fields of characteristic zero — Equal characteristic case

Rédei polynomials over fields of characteristic zero

The possible role of Rédei polynomials over fields of characteristic zero in the quest for solutions to problems in the study of geometries and vector spaces over finite fields is discussed. This note is exploratory and does not attempt to solve any particular problem, although an example problem is considered.

Model Theory of Fields with Free Operators in Characteristic Zero

Generalising and unifying the known theorems for difference and differential fields, it is shown that for every finite free S-algebra D over a field A of characteristic zero the theory of D-fields has a model companion D -CF0 which is simple and satisfies the Zilber dichotomy for finite-dimensional minimal types.

Mordell-Lang for function fields in characteristic zero, revisited

We give an elementary proof of the function field (or geometric) case of the Mordell-Lang conjecture in characteristic zero.

Weight-monodromy Conjecture over Equal Characteristic Local Fields

The aim of this paper is to study certain properties of the weight spectral sequences of Rapoport-Zink by a specialization argument. By reducing to the case over finite fields previously treated by Deligne, we prove that the weight filtration and the monodromy filtration defined on the l-adic étale cohomology coincide, up to shift, for proper smooth varieties over equal characteristic local fie...

Chapter 1 Characteristic p methods in characteristic zero via ultraproducts