14 citations · 40 across the 14 of their papers we have counts for
18 papers
PAC fields and difference fields with generic automorphisms
Özlem Beyarslan, Piotr Kowalski
We study the existence of model companions after adjoining an automorphism to field theories in two complementary settings. For bounded PAC fields of characteristic zero containing…
On generic and supertight automorphisms
Piotr Kowalski, Pınar Uğurlu Kowalski
We show that generic automorphisms of stable groups are supertight in a strong sense. In particular, we obtain the existence of supertight automorphisms. We also answer a question…
PAC structures as invariants of finite group actions
Daniel Max Hoffmann, Piotr Kowalski
We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invar…
Galois actions of finitely generated groups rarely have model companions
Özlem Beyarslan, Piotr Kowalski
We show that if is a finitely generated group such that its profinite completion is ``far from being projective'' (that is the kernel of the universal Frattini co…
Operators coming from ring schemes
Jakub Gogolok, Piotr Kowalski
We introduce the notion of a coordinate -algebra scheme and the corresponding notion of a -operator. This class of operators includes endomorphisms and der…
Model theory of fields with finite group scheme actions
Daniel Max Hoffmann, Piotr Kowalski
We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which general…
Model theory of Galois actions of torsion Abelian groups
Özlem Beyarslan, Piotr Kowalski
We show that the theory of Galois actions of a torsion Abelian group is companionable if and only if for each prime , the -primary part of is either finite or it coin…
Difference sheaves and torsors
Marcin Chałupnik, Piotr Kowalski
We develop sheaf theory in the context of difference algebraic geometry. We introduce categories of difference sheaves and develop the appropriate cohomology theories. As specializ…
Model theory of fields with free operators in positive characteristic
Özlem Beyarslan, Daniel Max Hoffmann, Moshe Kamensky +1
We give algebraic conditions about a finite algebra over a perfect field of positive characteristic, which are equivalent to the companionability of the theory of fields with "…
Difference modules and difference cohomology
Marcin Chalupnik, Piotr Kowalski
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding…
Three solutions for elliptic Dirichlet boundary value problem with singular weight
Piotr Kowalski, Joanna Piwnik
In this paper we prove the~existence of two non-trivial weak solutions of Dirichlet boundary value problem for p-Laplacian problem with a~singular part and two disturbances satisfy…
Existentially closed fields with finite group actions
Daniel Max Hoffmann, Piotr Kowalski
We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a…
A note on integrating group scheme actions
Daniel Hoffmann, Piotr Kowalski
We prove a non-integrability result concerning iterative derivations on projective line, where the iterative rule is given by a non-algebraic formal group.
Strongly minimal reducts of valued fields
Piotr Kowalski, Serge Randriambololona
We prove that if a strongly minimal non-locally modular reduct of an algebraically closed valued field of characteristic 0 contains +, then this reduct is bi-interpretable with the…
Existentially closed fields with G-derivations
Daniel Hoffmann, Piotr Kowalski
We prove that the theories of fields with Hasse-Schmidt derivations corresponding to actions of formal groups admit model companions. We also give geometric axiomatizations of thes…
Ax-Schanuel condition in arbitrary characteristic
Piotr Kowalski
We prove a positive characteristic version of Ax's theorem on the intersection of an algebraic subvariety and an analytic subgroup of an algebraic group. Our result is stated in a…
Three solutions to discrete anisotropic problems with two parameters
Marek Galewski, Piotr Kowalski
In this note we derive a type of a three critical point theorem which we further apply to investigate the multiplicity of solutions to discrete anisotropic problems with two parame…
Integrating Hasse-Schmidt derivations
Daniel Hoffmann, Piotr Kowalski
We study integrating (that is expanding to a Hasse-Schmidt derivation) derivations, and more generally truncated Hasse-Schmidt derivations, satisfying iterativity conditions given…