Related papers: Mordell-Lang in positive characteristic

We study the relative growth of finitely generated subgroups in finitely generated groups, and the corresponding distortion function of the embeddings. We explore which functions are equivalent to the relative growth functions and…

We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for virtually solvable groups.

In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.

Every endofunctor of the category of classes is proved to be set-based in the sense of Aczel and Mendler, therefore, it has a final coalgebra. Other basic properties of these endofunctors are proved, e.g. the existence of a free completely…

This paper contains the results of my PhD-thesis. I will show the K- and L-theoretic Farrell-Jones conjecture (FJC) for the general linear groups over the rationals and over the rational functions over a finite field. This especially…

We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)-space.

We provide a pure algebraic version of the dynamical characterization of Conrad's property. This approach allows dealing with general group actions on totally ordered spaces. As an application, we give a new and somehow constructive proof…

We give a conditional proof of the Uniform Boundedness Conjecture of Morton and Silverman in the case of polynomials over number fields, assuming a standard conjecture in arithmetic geometry. Our technique simultaneously yields a dynamical…

We prove the K-theoretic Farrell-Jones conjecture with (twisted) coefficients for CAT(0)-groups.

In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.

We prove a variant of the well-known Reidemeister-Schreier theorem for finitely $L$-presented groups. More precisely, we prove that each finite index subgroup of a finitely $L$-presented group is itself finitely $L$-presented. Our proof is…

We present a new algorithm deciding if the intersection of a quasiconvex subgroup of a negatively curved group with a conjugate is finite. We also give a short proof of decidability of the membership problem for quasiconvex subgroups of…

We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of quasiprojective varieties X, endowed with the action of a morphism f:X --> X. We use an analytic method based on the technique of Skolem, Mahler, and Lech,…

We initiate the study of finite characterizations and exact learnability of modal languages. A finite characterization of a modal formula w.r.t. a set of formulas is a finite set of finite models (labelled either positive or negative) which…

We present the notions of positively complete theory and general forms of amalgamation in the framework of positive logic. We explore the fundamental properties of positively complete theories and study the behaviour of companion theories…

It is proved that all finitely generated subgroups of generalized free product of two groups are finitely separable provided that free factors have this property and amalgamated subgroups are normal in corresponding factors and satisfy the…

A new type of conjectures on characters of finite groups, related to the McKay conjecture, have recently been proposed. In this paper, we study these conjectures for symmetric groups.

This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank discussed in [16]. Crucially,…

In this paper, we study the set of positive integers that characterize the universality of $m$-gonal form.

Let G be a Lie group over a local field of positive characteristic which admits a contractive automorphism f (i.e., the forward iterates f^n(x) of each group element x converge to the neutral element 1). We show that then G is a torsion…