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Derived from
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20402095 AL420 - ALGEBRAIC THEORY OF NUMBERS in Mathematics LM-40 PAPPALARDI FRANCESCO
(syllabus)
1. Introduction. Reviews on Number Fields. Traces, Norms and Discriminant. Rings of integers.
2. Commutative Algebra. Noetherian rings and Dedekind rings. The ζ function of Dedekind.
3. Algebra. Finitely generated groups and reviews of Theory of Galois. Lattices.
4. Discriminant and Ramification. The Minkowsi Theorem. Dirichlet's Theorem. The Group of classes and the finiteness of the class group.
5. The class number formula.
(reference books)
Schoof, R., Algebraic Number Theory. dispense Università di Roma Tor Vergata, http://www.mat.uniroma2.it/ ̃eal/moonen.pdf, (2003).
Milne, J., Algebraic Number Theory. Lecture Notes, http://www.jmilne.org/math/CourseNotes/ANT.pdf, (2017).
Marcus, D, Number fields, 3rd Ed. Springer-Verlag, (1977)
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