Related papers: The Hasse norm principle for abelian extensions

We prove limit theorems for row sums of a rowwise independent infinitesimal array of random variables with values in a locally compact Abelian group. First we give a proof of Gaiser's theorem, since it does not have an easy access and it is…

Soit $K$ un corps global et $G$ un $K$-groupe fini r\'esoluble. Sous certaines hypoth\`eses sur une extension d\'eployant $G$, on d\'emontre que l'espace homog\`ene $V:=G'/G$ avec $G'$ un $K$-groupe semi-simple simplement connexe v\'erifie…

Recently, the first two authors proved the Alon-Jaeger-Tarsi conjecture on non-vanishing linear maps, for large primes. We extend their ideas to address several other related conjectures. We prove the weak Additive Basis conjecture proposed…

Wirsing's theorem on approximating algebraic numbers by algebraic numbers of bounded degree is a generalization of Roth's theorem in Diophantine approximation. We study variations of Wirsing's theorem where the inequality in the theorem is…

We investigate the norm maps of algebraic even $K$-groups of finite extensions of number fields. Namely, we show that they are surjective in most situations. In the event that they are not surjective, we give a criterion in determining when…

A partial difference set $S$ in a finite group $G$ satisfying $1 \notin S$ and $S = S^{-1}$ corresponds to an undirected strongly regular Cayley graph ${\rm Cay}(G,S)$. While the case when $G$ is abelian has been thoroughly studied, there…

In a recent paper, Colliot-Th\'el\`ene, Parimala and Suresh conjectured that a local-global principle holds for projective homogeneous spaces of connected linear algebraic groups over function fields of p-adic curves. In this paper, we show…

Let $K$ be a complete discrete valuation field of characteristic $0$ with not necessarily perfect residue field of characteristic $p>0$. We define a Faltings extension of $\mathcal{O}_K$ over $\mathbb{Z}_p$, and we construct a Hodge-Tate…

After a brief introduction to the classical theory of binary quadratic forms we use these results for proving (most of) the claims made by P\'epin in a series of articles on unsolvable quartic diophantine equations, and for constructing…

Let $A$ be an abelian variety over a field finitely generated over $\mathbb{Q}$. We show that the finiteness of the $\ell$-primary torsion subgroup of the higher Brauer group is a sufficient criterion for the Tate conjecture to hold.…

A seminal result of H\r{a}stad [J. ACM, 48(4):798--859, 2001] shows that it is NP-hard to find an assignment that satisfies $\frac{1}{|G|}+\varepsilon$ fraction of the constraints of a given $k$-LIN instance over an abelian group, even if…

For a fixed finite solvable group $G$ and number field $K$, we prove an upper bound for the number of $G$-extensions $L/K$ with restricted local behavior (at infinitely many places) and ${\rm inv}(L/K)<X$ for a general invariant $"{\rm…

The problem of estimating the exponent of a stable law received a considerable attention in the recent literature. Here, we deal with an estimate of such a exponent introduced by De Haan and Resnick when the corresponding distribution…

We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each…

Given a field $k$ and a finite group $H$, {\it{an $H$-parametric extension over $k$}} is a finite Galois extension of $k(T)$ of Galois group containing $H$ which is regular over $k$ and has all the Galois extensions of $k$ of group $H$…

We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian…

We describe how previously known methods for determining the number of decimation classes of density $\delta$ binary vectors can be extended to nonnegative integer vectors, where the vectors are indexed by a finite abelian group $G$ of size…

Let $\Delta$ be a root system with a subset of positive roots, $\Delta^+$. We consider edges of the Hasse diagrams of some posets associated with $\Delta^+$. For each edge one naturally defines its type, and we study the partition of the…

Using functional and harmonic analysis methods, we study Kazhdan sets in topological groups which do not necessarily have Property (T). We provide a new criterion for a generating subset $Q$ of a group $G$ to be a Kazhdan set; it relies on…

We show that, for an abelian variety defined over a $p$-adic field $K$ which has potential good reduction, its torsion subgroup with values in the composite field of $K$ and a certain Lubin-Tate extension over a $p$-adic field is finite.