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This second part of the paper strengthens the descent theory described in the first part to rational maps, arbitrary base fields, and dynamics given by correspondences. We obtain in particular a decomposition of any difference field extension into a tower of finite, field-internal and one-based difference field extensions. This is needed in order to obtain the dynamical Northcott Theorem 1.11 of Part I in sharp form.
We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all completions of the
We prove field quantifier elimination for valued fields endowed with both an analytic structure and an automorphism that are $sigma$-Henselian. From this result we can deduce various Ax-Kochen-Ersov type results with respect to completeness and the N
We construct a semi-orthogonal decomposition on the category of perfect complexes on the blow-up of a derived Artin stack in a quasi-smooth centre. This gives a generalization of Thomasons blow-up formula in algebraic K-theory to derived stacks. We a
We initiate the study of p-adic algebraic groups G from the stability-theoretic and definable topological-dynamical points of view, that is, we consider invariants of the action of G on its space of types over Q_p in the language of fields. We consid
Let us consider an algebraic function field defined over a finite Galois extension $K$ of a perfect field $k$. We give some conditions allowing the descent of the definition field of the algebraic function field from $K$ to $k$. We apply these result