Logo

Lectures on Field Theory and Ramification Theory

Small book cover: Lectures on Field Theory and Ramification Theory

Lectures on Field Theory and Ramification Theory
by

Publisher: Indian Institute of Technology, Bombay
Number of pages: 36

Description:
These are the notes of a series of five lectures, aimed at covering the essentials of Field Theory and Ramification Theory as may be needed for local and global class field theory. Included are the two sections on cyclic extensions and abelian extensions.

Home page url

Download or read it online for free here:
Download link
(360KB, PDF)

Similar books

Book cover: Galois Theory: Lectures Delivered at the University of Notre DameGalois Theory: Lectures Delivered at the University of Notre Dame
by - University of Notre Dame
The book deals with linear algebra, including fields, vector spaces, homogeneous linear equations, and determinants, extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, and more.
(2775 views)
Book cover: Notes on Galois TheoryNotes on Galois Theory
by - Boston College
From the table of contents: Basic ring theory, polynomial rings; Finite fields; Extensions of rings and fields; Computing Galois groups of polynomials; Galois groups and prime ideals; Cyclotomic extensions and abelian numbers.
(5731 views)
Book cover: Class Field TheoryClass Field Theory
by
Class field theory describes the abelian extensions of a local or global field in terms of the arithmetic of the field itself. These notes contain an exposition of abelian class field theory using the algebraic/cohomological approach.
(8072 views)
Book cover: Lectures On Galois Cohomology of Classical GroupsLectures On Galois Cohomology of Classical Groups
by - Tata Institute of Fundamental Research
The main result is the Hasse principle for the one-dimensional Galois cohomology of simply connected classical groups over number fields. For most groups, this result is closely related to other types of Hasse principle.
(6616 views)