Related papers: Notes on abelian class field theory
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…
In this expository article we present Rosenlicht's work on geometric class field theory, which classifies abelian coverings of smooth, projective, geometrically connected curves over perfect fields.
We study the distribution of algebraic points on curves in abelian varieties over finite fields.
We prove control theorems for abelian varieties over function fields.
We provide a characterization of almost ordinary abelian varieties over finite fields, and use this characterization to provide lower bounds for the sizes of some almost ordinary isogeny classes.
We investigate the large values of class numbers of cubic fields, showing that one can find arbitrary long sequences of "close" abelian cubic number fields with class numbers as large as possible. We also give a first step toward an…
In a stable abelian group, we characterize generic types of cosets of type-definable subgroups.
A pedagological introduction to effective field theory is presented.
These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.
We study isogeny classes of abelian varieties over a function field in one variable over the field of complex numbers.
In these notes we provide the foundation for the deformation theoretic parts of arXiv:0807.3753 and arXiv:math/0102005.
Lecture notes for an introductory course in elementary particles.
These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.
In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.
In this paper, we classify the possible group structures on the set of $R$-valued points of an abelian variety, where $R$ is any real closed field. We make use of a family of abelian varieties that, in effect, allows one to quantify over…
In this note some properties of the sum of element orders of a finite abelian group are studied.
We develop class field theory of curves over $p$-adic fields which extends the unramified theory of S. Saito. The class groups which approximate abelian \'etale fundamental groups of such curves are introduced in the terms of algebraic…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $k$-isogeny class.
This paper is a review of the theory of abelian anyons in planar systems at an introductory level and with focus on the formalism of quantum field theory, but with the aim of clarify the connections between the mathematical structure and…