Related papers: On wild ramification in quaternion extensions

We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…

We use techniques of relative algebraic K-theory to develop a common refinement of the existing theories of metrized and hermitian Galois structures in arithmetic. As a first application of this very general approach, we then use it to…

Higher extensions and higher central extensions, which are of importance to non-abelian homological algebra, are studied, and some fundamental properties are proven. As an application, a direct proof of the invariance of the higher Hopf…

We review a lattice construction arising from quaternion algebras over number fields and use it to obtain some known extremal and densest lattices in dimensions 8 and 16. The benefit of using quaternion algebras over number fields is that…

This paper extends Hopf-Galois theory to infinite field extensions and provides a natural definition of subextensions. For separable (possibly infinite) Hopf-Galois extensions, it provides a Galois correspondence. This correspondence also…

The theorem of factorisation forests shows the existence of nested factorisations -- a la Ramsey -- for finite words. This theorem has important applications in semigroup theory, and beyond. The purpose of this paper is to illustrate the…

Let $F$ be a totally real field of degree $g$, and let $p$ be a prime number. We construct $g$ partial Hasse invariants on the characteristic $p$ fiber of the Pappas-Rapoport splitting model of the Hilbert modular variety for $F$ with level…

In this article, we introduce the notion of free subexponentiality, which extends the notion of subexponentiality in the classical probability setup to the noncommutative probability spaces under freeness. We show that distributions with…

We construct a counterexample to a well-known extension theorem for slice regular functions, which motivates us to develop a theory of Riemann slice-domains by introducing a new topology on quaternions. By some paths describing axial…

This paper deals with extension of analytic covers. We prove topological extension theorems for analytic covers. The main result is an extension theorem which only uses the extension of the ramification divisor. We give also a Thullen-type…

Let $G$ be a finite nilpotent group and $K$ a number field with torsion relatively prime to the order of $G$. By a sequence of central group extensions with cyclic kernel we obtain an upper bound for the minimum number of prime ideals of…

A finite separable extension of a field is called primitive if there are no intermediate extensions. The most interesting primitive extensions of a local field with finite residue field are the wildly ramified ones, and our aim here is to…

For a prime number $\ell$ and an extension of number fields $K/F$, we prove new lower bounds on the $\ell$-rank of the ideal class group of $K$ based on prime ramification in $K/F$. Unlike related results from the literature, our bound is…

Let K be a maximal unramified extension of a nonarchimedean local field with arbitrary residual characteristic p. Let G be a reductive group over K which splits over a tamely ramified extension of K. We show that the associated Moy-Prasad…

We extend classical results on simple varieties of trees (asymptotic enumeration, average behavior of tree parameters) to trees counted by their number of leaves. Motivated by genome comparison of related species, we then apply these…

We discuss several extension properties of matroids and polymatroids and their application as necessary conditions for the existence of different matroid representations, namely linear, folded linear, algebraic, and entropic…

We associate two linear categories with two objects to a module over the subalgebra of coinvariants of a Hopf-Galois extension, and prove that they are isomorphic. The structure Theorem for cleft extensions, and the Militaru \cStefan…

We study Galois extensions Coinv(M)<M for M an H-comodule algebra and H a Frobenius Hopf algebroid. We obtain generalizations of various theorems in Hopf-Galois theory by Kreimer-Takeuchi, Doi-Takeuchi and Cohen-Fischman-Montgomery. An…

Firstly, bilinear Fourier Restriction estimates --which are well-known for free waves-- are extended to adapted spaces of functions of bounded quadratic variation, under quantitative assumptions on the phase functions. This has applications…

A cover of normal varieties is exceptional over a finite field if the map on points over infinitely many extensions of the field is one-one. A cover over a number field is exceptional if it is exceptional over infinitely many residue class…