Related papers: The theory of maximal Hardy fields
It is shown that light front thermal field theory is equivalent to conventional thermal field theory. The proof is based on the use of spectral representations, and applies to all Lagrangians for which such equivalence has been proven at…
We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.
We prove the following variant of Helly's classical theorem for Hamming balls with a bounded radius. For $n>t$ and any (finite or infinite) set $X$, if in a family of Hamming balls of radius $t$ in $X^n$, every subfamily of at most…
We study analogues of Tate's conjecture on homomorphisms for abelian varieties when the ground field is finitely generated over an algebraic closure of a finite field. Our results cover the case of abelian varieties without nontrivial…
We show that the category of motivic spaces with transfers along finite flat morphisms, over a perfect field, satisfies all the properties we have come to expect of good categories of motives. In particular we establish the analog of…
Let $\textbf{k}$ be an algebraically closed field. We classify all maximal $\textbf{k}$-subalgebras of any one-dimensional finitely generated $\textbf{k}$-domain. In dimension two, we classify all maximal $\textbf{k}$-subalgebras of…
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
We give a short proof of an inequality, conjectured by Tsfasman and proved by Serre, for the maximum number of points on hypersurfaces over finite fields. Further, we consider a conjectural extension, due to Tsfasman and Boguslavsky, of…
Motivated by previous work leveraging factorizations of second- and fourth-order differential operators, a general integral inequality involving higher order derivatives is proven by elementary means. It is then shown how this framework…
We solve the inverse differential Galois problem over differential fields with a large field of constants of infinite transcendence degree over ${\mathbb Q}$. More generally, we show that over such a field, every split differential…
We give a criterion for maps on ultrametric spaces to be surjective and to preserve spherical completeness. We show how Hensel's Lemma and the multi-dimensional Hensel's Lemma follow from our result. We give an easy proof that the latter…
As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of \textbf{two} matrices. So it is fundamental to study first the centralizer algebra of a single matrix, called a centralizer matrix…
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
A new twistorial field formulation of a massless infinite spin particle is derived. We find a twistorial infinite spin field and derive its helicity decomposition. The twistorial equations of motion for infinite spin fields in the cases of…
We classify Artin-Schreier extensions of valued fields with non-trivial defect according to whether they are connected with purely inseparable extensions with non-trivial defect, or not. We use this classification to show that in positive…
We propose a manifestly supersymmetric generalization of the solvable $T \overline{T}$ deformation of two-dimensional field theories. For theories with $(1,1)$ and $(0,1)$ supersymmetry, the deformation is defined by adding a term to the…
Our main theorem asserts that every Farey graph embedded in the 1-skeleton of the pants complex of any finite type surface is totally geodesic.
We use higher ideles and duality theorems to develop a universal approach to higher dimensional class field theory.
We construct N=1 supersymmetric field theory in 4+2 dimensions compatible with the theoretical framework of 2T physics and its gauge symmetries. The fields are arranged into 4+2 dimensional chiral and vector supermultiplets, and their…
We give an elementary construction of an arbitrary differentially closed field and of a universal differential extension of a differential field in terms of Nash function fields. We also give a characterization of any Archimedean ordered…