18.785 Number Theory I, Fall 2019
Author(s)
Sutherland, Andrew
Alternative Title
Number Theory I
Date Issued
December 2019
Abstract
This is the first semester of a one-year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.
Subjects
Absolute values
Discrete valuations
localization
Dedekind domains
Etale algebras
Dedekind extensions
Ideal Norm
Dedekind-Kummer Theorem
Galois extensions
Artin map
complete fields
Valuation rings
Hensel's lemmas
Krasner's lemma
Minkowski bound
Dirichlet's unit theorm
Zeta function
Ray Class
Ring of Adeles
Idele group
Chebotarev density theorem
Global fields
Tate cohomology
Artin reciprocity
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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