ALGANT STUDENT SEMINAR – NUMBER THEORY COURSE
Date and time: Monday, June 13th, at 12.30
Room: aula 9
Andrea Berti
Title: Adeles, Ideles and a first look at Global Class Field Theory.
Abstract: This lecture is divided into two parts.
In the first part we will develop tools for an adelic/idelic approach to number theory. More in detail, we will introduce restrict topological product to define Adeles/Ideles, we will state and discuss Strong Approximation Theorem and give an Idelic interpretation of the Ray Class Groups of a number field. Time permitting, we will also give, as application, either a proof of the finiteness of the Class Group of a number field or of the Dirichlet’s Unit Theorem.
In the second part we will introduce the Global case of Class Field Theory, trying to understand (at least the statement of) the Global Reciprocity Law.
References:
[1] Cassels, J. W. S., and A. Froehlich, Algebraic Number Theory, Academic Press (1967).
[2] J.S. Milne Class Field Theory, Online notes avaible at http://www.jmilne.org/math/CourseNotes/cft.html
[3] GJ Janusz, “Algebraic Number Fields,” Academic Press, New York (1973).