Course Archives Theoretical Statistics and Mathematics Unit
Course: Algebraic Number Theory
Level: Postgraduate
Time: Currently not offered
Past Exams


(Note: A priori knowledge of Commutative Algebra is desirable.)
Algebraic numbers and algebraic integers; Brief review of integral extensions; Norm, trace and discriminant; Existence of integral basis. Dedekind domains, ideal class group. Minkowsky theory, finiteness of class group. Dirichlet unit theorem. Factoring of prime ideals on extensions, fundamental identity; Quadratic number fields (computation of class numbers, prime decomposition, Pells equa tions). Hilberts ramification theory (decomposition and inertia groups); Cyclo tomic fields. Valuations, completions, local fields

Suggested Texts :
(a) G.J. Janusz: Algebraic Number Fields, (chapter 1-4), AMS (1996).
(b) D.A. Marcus: Number Fields, Springer-Verlag (1977).
(c) J. Neukirch: Algebraic Number Theory, Springer (1999).
(d) P. Ribenboim: Classical Theory of Algebraic Numbers, Springer Science and Business Media (2001).
(e) J. Esmonde and M. Ram Murty: Problems in Algebraic Number Theory, Springer (Indian reprint 2006).
(f) TIFR pamphlet on Algebraic Number Theory.

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