Number Theory Lecture Notes by Andrew Sutherland

This
note in number theory explains standard topics in algebraic and analytic number
theory. Topics covered includes: Absolute values and discrete valuations,
Localization and Dedekind domains, ideal class groups, factorization of ideals,
Etale algebras, norm and trace, Ideal norms and the Dedekind-Kummer
thoerem, Galois extensions, Frobenius elements, Complete fields and valuation
rings, Local fields and Hensel's lemmas , Extensions of complete DVRs,
Totally ramified extensions and Krasner's lemma , Dirichlet's unit theorem,
Riemann's zeta function and the prime number theorem, The functional equation ,
Dirichlet L-functions and primes in arithmetic progressions, The analytic class
number formula, The Kronecker-Weber theorem, Class field theory, The main
theorems of global class field theory, Tate cohomology, profinite groups,
infinite Galois theory, Local class field theory, Global class field theory and
the Chebotarev density theorem.

**Author(s):** Andrew Sutherland

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