Related papers: Notes on abelian class field theory

We give a function field specific, algebraic proof of the main results of class field theory for abelian extensions of degree coprime to the characteristic. By adapting some methods known for number fields and combining them in a new way,…

These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.

We give a new approach for the local class field theory of Serre and Hazewinkel. We also discuss two-dimensional local class field theory in this framework.

In this preliminary note we prove that the theory of valued fields equipped with an action of a given finite group has a model companion.

In this paper, using what we call a micro reciprocity law, we complete Weil's program for non-abelian class field theory of Riemann surfaces.

The note complements topological aspects of the theory of chiral algebras.

We give a proposal for future development of the model theory of valued fields. We also summarize some recent results on p-adic numbers.

We provide a short introduction to the main features of the algebraic approach to quantum field theories.

This thesis deals with the capitulation problem in class field theory and gives various new insights into the subject.

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.

We use knowledge of local fields to adapt Jonathan Lubin and Michael Rosen's proof of Mazur's Proposition 4.39. This changes the result about abelian varieties from only working over local fields with a finite residue field to working with…

These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.

In this note, we propose the modular height of an abelian variety defined over a field of finite type over Q. Moreover, we prove its finiteness property.

These notes are a written version of a set of lectures given at TASI-02 on the topic of effective field theories. They are meant as an introduction to some of the latest techniques and applications in the field.

We introduce the concept of the modularity of an abelian variety defined over the rational number field extending the modularity of an elliptic curve. We discuss the modularity of an abelian variety over the rational number field. We…

In this paper we find the genus field of finite abelian extensions of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the…

We give an asymptotic formula for class numbers of orders in cubic number fields.

We obtain a (Abelian) two form field as a connection on a flat space-time and its corresponding field strength is canonically constructed.

We describe an inductive approach most appropriate for abelian varieties with an action of an imaginary quadratic field.

These short lecture notes provide an introduction to some basic notions of F-theory with some special emphasis on its relation to Type IIB orientifolds with O7/O3-planes.