Acquire methods and techniques of modern algebraic theory of numbers through classic problems initiated by Fermat, Euler, Lagrange, Dedekind, Gauss, Kronecker.
teacher profile teaching materials
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.
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)
Mutuazione: 20402095 AL420 - TEORIA ALGEBRICA DEI NUMERI in Matematica LM-40 PAPPALARDI FRANCESCO
Programme
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.
Core Documentation
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)
Type of delivery of the course
48 hours of lectures and 12 hours of problem sessionsAttendance
suggestedType of evaluation
Individual exercises to be carried out at home and presentation of a seminar