Related papers: Fermats Last Theorem on Topological Fields

We give a reformuation of the Tate conjecture for a surface over a finite field in terms of suitable affine open subsets. We then present three attempts to prove this reformulation, each of them falling short. Interestingly, the last two…

A convenient technique for calculating completed topological tensor products of functional Frechet or DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire…

We establish a generalization of Luttinger's theorem that applies to fractionalized Fermi liquids, i.e. Fermi liquids coexisting with symmetry enriched topological order. We find that, in the linear relation between the Fermi volume and the…

We quantify Peter Scott's Theorem that surface groups are locally extended residually finite (LERF) in terms of geometric data. In the process, we will quantify another result by Scott that any closed geodesic in a surface lifts to an…

We formulate and analyze several finiteness conjectures for linear algebraic groups over higher-dimensional fields. In fact, we prove all of these conjectures for algebraic tori as well as in some other situations. This work relies in an…

This paper is the second in a series of three, the aim of which is to construct algebraic geometry over a free metabelian Lie algebra $F$. For the universal closure of free metabelian Lie algebra of finite rank $r \ge 2$ over a finite field…

In this paper, with the help of the theory of matrices and finite fields we generalize Zolotarev's theorem to an arbitrary finite dimensional vector space over $\mathbb{F}_q$, where $\mathbb{F}_q$ denotes the finite field with $q$ elements.

Results about the structure of the set of Egyptian fractions on the line are extended to subsets of topological groups.

Number of results in number theory have been developed using a new method. The Goldbach binary conjecture in strengthened formulation have been among them.

The main aim of the present paper is to represent an exact and simple proof for FLT by using properties of the algebra identities and linear algebra.

Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…

Thermoluminescence (TL) kinetics in spatially inhomogeneous systems can be studied by various Monte Carlo algorithms. Recently, a new analytical approach was suggested for the isolated cluster model. The theory is based on the concept of…

The Lowest Landau Level (LLL), long distance theory of Composite Fermions (CF) developed by Murthy and myself is minimally extended to all distances, guided by very general principles. The resulting theory is mathematically consistent, and…

Infinite dimensional Hamiltonian systems appear naturally in the rich algebraic structure of Symplectic Field Theory. Carefully defining a generalization of gravitational descendants and adding them to the picture, one can produce an…

We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in…

We show how topology of a space may lead to tensor fields on (the smooth part of) moduli spaces of the fundamental group.

Through the question of singular topologies in the Boulatov model, we illustrate and summarize some of the recent advances in Group Field Theory.

We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…

This is an expository note discussing how the Erdos--Ramanujan proof of Bertrand's postulate may be adapted to show the existence of finite fields.

We prove that two arithmetically significant extensions of a field F coincide if and only if the Witt ring WF is a group ring Z/n[G]. Furthermore, working modulo squares with Galois groups which are 2-groups, we establish a theorem…