Arithmetic Geometry
A.Y. 2026/2027
Learning objectives
The goal of the course is to provide an introduction to the theory of modular forms and of L-functions, complex and p-adic.
Expected learning outcomes
We expect that students will get familiarity with the theory of modular forms and of L-functions.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Action of SL(2,Z) on the Poincarè upper half plane, construction of modular curves and their moduli interpretation, modular forms, q-expansions, examples: theta functions and Eisenstein series. Riemann zeta function, Dirichlet L-functions, Kubota-Leopoldt p-adic L-functions.
Prerequisites for admission
Holomorphic functions. Covers and universal cover of surfaces.
Teaching methods
Lectures in presence.
Teaching Resources
J.-P. Serre: A Course in Arithmetic, GTM vol. 7
Cassels and Frohlich "Algebraic number theory"
P. Colmez, "Fontaine's rings and p-adic L-functions"
Cassels and Frohlich "Algebraic number theory"
P. Colmez, "Fontaine's rings and p-adic L-functions"
Assessment methods and Criteria
Seminar on a topic chosen by the student and proposed by the professors.
MATH-02/A - Algebra - University credits: 3
MATH-02/B - Geometry - University credits: 3
MATH-02/B - Geometry - University credits: 3
Lessons: 42 hours
Professors:
Andreatta Fabrizio, Seveso Marco Adamo
Professor(s)