MA 5150: Algebraic Number Theory

All the updates related to MA 5150 are announced here.

### Class timings:

Tuesday: 08:30 am to 10:00 am

Thursday: 02:30 pm to 04:00 pm

### Examination and Grades:

The grades will be decided by the marks obtained in the surprise tests, mid-term, final examination, and also by the performance in the class.

## Syllabus:

Localisation, Integral ring extensions, Dedekind domains, discrete valuation rings, unique factorisation of ideals, ideal class groups, finiteness of class number, some class number computations, valuations and completions of number fields, Hensel's lemma, norm, trace, discriminant, different, Ramification theory of p-adic fields, Decomposition groups, Inertia groups, cyclotomic fields, Gauss sums, quadratic reciprocity, geometry of numbers, Ostrowski's theorem, Dirichletâ€™s unit theorem.

#### Pre-requisite courses:

MA 4070, MA 5070.
## References:

- Janusz, Gerald J. Algebraic number fields. Second edition. Graduate Studies in Mathematics, 7. American Mathematical Society, Providence, RI, 1996.
- Lang, Serge. Algebraic number theory. Second edition. Graduate Texts in Mathematics, 110. Springer-Verlag, New York, 1994.
- Marcus, Daniel A. Number fields. Universitext. Springer-Verlag, New York-Heidelberg, 1977.

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