Related papers: A note on valued fields with finite group actions

Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.

These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…

We prove some results about the model theory of fields with a derivation of the Frobenius map, especially that the model companion of this theory is axiomatizable by axioms used by Wood in the case of the theory $\operatorname{DCF}_p$ and…

In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…

Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a…

We prove the rationality of some zeta functions associated tocharacters of pro-p groups of finite rank.

A model companion is shown to exist for the theory of partial differential fields of characteristic zero equipped with free operators that commute with the derivations. The free operators here are those introduced in [R. Moosa and T.…

In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.

The article motivates, presents and describes large computer calculations concerning the asymptotic behaviour of arithmetic properties of coefficient fields of modular forms. The observations suggest certain patterns, which deserve further…

This note presents Galois theory for finite fields. It was written as a handout for the MAT401 course ``Polynomial equations and fields'' taught at the University of Toronto in Spring 2026. We use without proofs some basic properties of…

We propose graph theoretic equivalents for existence of a finite projective plane. We then develop a new approach and see that the problem of existence of a finite projective plane of order n is linked up with a subset of sharply 2…

We study unirational algebraic varieties and the fields of rational functions on them. We show that after adding a finite number of variables some of these fields admit an infinitely transitive model. The latter is an algebraic variety with…

A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.

For a simple, normal and finite extension of a valued field, we prove that we can related the order of the ramification group of the field extension and the set of key polynomials associated to the extension of the valuation. More…

We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.

If $G$ is a finite $\ell$-group acting on an affine space $\mathbb{A}^n$ over a finite field $K$ of cardinality prime to $\ell$, Serre has shown that there exists a rational fixed point. We generalize this to the case where $K$ is a…

The study of many problems in additive combinatorics, such as Szemer\'edi's theorem on arithmetic progressions, is made easier by first studying models for the problem in F_p^n for some fixed small prime p. We give a number of examples of…

We introduce higher-order support varieties for pairs of modules over a commutative local complete intersection ring, and give a complete description of which varieties occur as such support varieties. In the context of a group algebra of a…

We prove a character sum identity for Coxeter arrangements which is a finite field analogue of Macdonald's conjecture proved by Opdam.

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…