Examination Schedule :
- Quiz 1: Scheduled on Tuesday, February 7, 2012 at 9.00 AM
- Mid-Sem Exam: Scheduled on Saturday, February 25, 2012 at 11.00 AM
Course Contents of MA 524 Algebraic Number Theory
| ||Credit Structure: 2 1 0 6
||Prerequisites : MA 505: Algebra-II (Exposure)
Algebraic number fields.
Localisation, discrete valuation rings.
Integral ring extensions, Dedekind domains,
unique factorisation of ideals.
Action of the
galois group on prime ideals.
Valuations and completions of number fields,
discussion of Ostrowski's theorem,
lemma, unramified, totally ramified and
tamely ramified extensions of p-adic fields.
Discriminants and Ramification.
Cyclotomic fields, Gauss sums, quadratic
The ideal class group, finiteness of the ideal
class group, Dirichlet units theorem.
Texts / References
K. Ireland and M. Rosen, A Classical Introduction to
Modern Number Theory, 2nd ed., Springer-Verlag, 1990.
S. Lang, Algebraic Number Theory, Addison-Wesley, 1970.
D.A. Marcus, Number Fields, Springer-Verlag, 1977.
Apart from these, we shall refer to the Kiel Notes, which are available
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