Related papers: The Capitulation Problem in Class Field Theory
The text is a synthetic presentation of the state of the knowledge about the capitulation for the class-groups of numbers fields, shortly before the demonstration by Suzuki of the main conjecture on this question.
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
We give a presentation of abelian class field theory.
This is a brief introduction to the subject of Conformal Field Theory on surfaces with boundaries and crosscaps, which describes the perturbative expansion of open string theory.
We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the…
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields. We also discuss capitulation of the minus part and the…
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
Let \(\Gamma=\mathbb{Q}(\sqrt[3]{n})\) be a pure cubic field with normal closure \(k=\mathbb{Q}(\sqrt[3]{n},\zeta)\), where \(n>1\) denotes a cube free integer, and \(\zeta\) is a primitive cube root of unity. Suppose \(k\) possesses an…
We reduce the classification of finite extensions of function fields (of curves over finite fields) with the same class number to a finite computation; complete this computation in all cases except when both curves have base field…
In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the…
In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.
We prove a capitulation result for locally free class groups of orders of group algebras over number fields. As a corollary, we obtain an "arithmetically disjoint capitulation result" for the Galois module structure of rings of integers.
We discuss a few selected topics in finite temperature field theory.
This work contains a set of lectures on defect structures, mainly in models described by scalar fields in diverse dimensions.
The modern theory of class field towers has its origins in the study of the p-class field tower over a quadratic imaginary number field, so it is fitting that this problem be the first in the discipline to be nearing a solution. We survey…
A comprehensive introduction to two-dimensional conformal field theory is given.
In this paper, we establish two main results which give conditions necessary and sufficient for a $ 2 $-group metabelian such that $G/G'$ is of type $(2, 4)$ either metacyclic or not. If $G$ is the Galois group of…
Recently, a new approach, based on boundary conformal field theory, has been applied to a variety of quantum impurity problems in condensed matter and particle physics. A particularly enlightening example is the multi-channel Kondo problem.…
This Thesis is devoted to the analysis of entanglement in relevant physical systems. Entanglement is the conducting theme of this research, though I do not dedicate to a single topic, but consider a wide scope of physical situations. I have…