Number Theory II: Class Field Theory

A commutative diagram consisting of 4-row 3-column grids.

Commutative diagram: the map φ is surjective by the choice of S and is also injective by the definition of ESx. (Courtesy of Oron Propp. Used with permission.)


MIT Course Number


As Taught In

Spring 2016



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Course Description

Course Features

Course Description

This course is the continuation of 18.785 Number Theory I. It begins with an analysis of the quadratic case of Class Field Theory via Hilbert symbols, in order to give a more hands-on introduction to the ideas of Class Field Theory. More advanced topics in number theory are discussed in this course, such as Galois cohomology, proofs of class field theory, modular forms and automorphic forms, Galois representations, and quadratic forms.

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This is a graduate-level course in Algebraic Number Theory. The content varies year to year, according to the interests of the instructor and the students.

Related Content

Sam Raskin. 18.786 Number Theory II: Class Field Theory. Spring 2016. Massachusetts Institute of Technology: MIT OpenCourseWare, License: Creative Commons BY-NC-SA.

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