Let K be a finite extension of Qp, let L/K be a finite abelian Galois extension of odd degree and let OL be the valuation ring of L. We define AL/K to be the unique fractional OL-ideal with square equal to the inverse different of L/K. For p an odd prime and L/Qp contained in certain cyclotomic extensions, Erez has described integral normal bases for AL/Qp that are self-dual with respect to the...

1 Preliminaries on monoids Definition 1.1. An Abelian monoid is a set with a binary, associative, and commutative operation which has a neutral element. It will often be called just a monoid in this manuscript because we will not deal with non-commutative monoids. A monoid M is called • finitely generated if there is a finite set of generators, or equivalently if there is a surjection of monoid...

The effective string action of the color-electric flux tube in the U(1)×U(1) dual Ginzburg-Landau (DGL) theory is studied by performing a path-integral analysis by taking into account the finite thickness of the flux tube. The DGL theory, corresponding to the low-energy effective theory of Abelian-projected SU(3) gluodynamics, can be expressed as a [U(1)]3 dual Abelian Higgs (DAH) model with a ...

We consider two families of weighted zero-sum constant for finite abelian groups. For a finite abelian group (G,+), a set of weights W ⊂ Z, and an integral parameter m, the m-wise Davenport constant with weights W is the smallest integer n such that each sequence over G of length n has at least m disjoint zero-subsums with weights W . And, for an integral parameter d, the d-constrained Davenpor...

We give a function F (d, n, p) such that if K/Qp is a degree n field extension and A/K is a d-dimensional abelian variety with potentially good reduction, then #A(K)[tors] ≤ F (d, n, p). Separate attention is given to the prime-to-p torsion and to the case of purely additive reduction. These latter bounds are applied to classify rational torsion on CM elliptic curves over number fields of degre...

Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility, accessible anyons with current technology all belong to a class that is called weakly integral—anyons whose squared quantum dimensions are integers. We analyze the co...

We introduce a tensor category O+ (resp. O−) of certain modules of ĝl∞ with non-negative (resp. non-positive) integral central charges with the usual tensor product. We also introduce a tensor category (Of , ⊙ ) consisting of certain modules over GL(N) for all N . We show that the tensor categories O± and Of are semisimple abelian and all equivalent to each other. We give a formula to decompose...

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

Higher order coefficients of the inverse mass expansion of one–loop effective actions are obtained from a one–dimensional path integral representation. For the evaluation of the path integral with Wick contractions a suitable Green function has to be chosen. We consider the case of a massive scalar loop in the background of both a scalar potential and a (non–abelian) gauge field. For the pure s...