Acquire methods and techniques of modern algebraic theory of numbers through classic problems initiated by Fermat, Euler, Lagrange, Dedekind, Gauss, Kronecker.
Curriculum
scheda docente
materiale didattico
Unique factorisation of ideals in the rings of integers.
Class group.
Group of units.
Fermat's last Theorem for regular primes
Local fields.
Marcus, D. Number fields, 3rd Ed Springer-Verlag. 1977.
Samuel, P. Théorie algébrique des nombres, Hermann, Paris. 1971.
Schoof, R. Algebraic Number Theory, dispense Università di Roma Tor Vergata, 2003.
Milne, J. Algebraic Number Theory, Lecture Notes, 2017.
Programma
Ring of integers in number fields.Unique factorisation of ideals in the rings of integers.
Class group.
Group of units.
Fermat's last Theorem for regular primes
Local fields.
Testi Adottati
Notes by the lecturer.Marcus, D. Number fields, 3rd Ed Springer-Verlag. 1977.
Samuel, P. Théorie algébrique des nombres, Hermann, Paris. 1971.
Schoof, R. Algebraic Number Theory, dispense Università di Roma Tor Vergata, 2003.
Milne, J. Algebraic Number Theory, Lecture Notes, 2017.
Modalità Erogazione
Lectures in class on blackboard and exercise classesModalità Valutazione
The exam will consist of an oral test in which the learning of the course program and the ability to solve exercises will be verified.
scheda docente
materiale didattico
Unique factorisation of ideals in the rings of integers.
Class group.
Group of units.
Fermat's last Theorem for regular primes
Local fields.
Marcus, D. Number fields, 3rd Ed Springer-Verlag. 1977.
Samuel, P. Théorie algébrique des nombres, Hermann, Paris. 1971.
Schoof, R. Algebraic Number Theory, dispense Università di Roma Tor Vergata, 2003.
Milne, J. Algebraic Number Theory, Lecture Notes, 2017.
Mutuazione: 20410520 AL420 - TEORIA ALGEBRICA DEI NUMERI in Matematica LM-40 R BARROERO FABRIZIO
Programma
Ring of integers in number fields.Unique factorisation of ideals in the rings of integers.
Class group.
Group of units.
Fermat's last Theorem for regular primes
Local fields.
Testi Adottati
Notes by the lecturer.Marcus, D. Number fields, 3rd Ed Springer-Verlag. 1977.
Samuel, P. Théorie algébrique des nombres, Hermann, Paris. 1971.
Schoof, R. Algebraic Number Theory, dispense Università di Roma Tor Vergata, 2003.
Milne, J. Algebraic Number Theory, Lecture Notes, 2017.
Modalità Erogazione
Lectures in class on blackboard and exercise classesModalità Valutazione
The exam will consist of an oral test in which the learning of the course program and the ability to solve exercises will be verified.