5 papers
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…
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…
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 "…
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…