Syllabus ELLIPTIC CURVES AND MODULAR FORMS - 80778
עברית
 Students needing academic accommodations based on a disability should contact the Center for Diagnosis and Support of Students with Learning Disabilities, or the Office for Students with Disabilities, as early as possible, to discuss and coordinate accommodations, based on relevant documentation. For further information, please visit the site of the Dean of Students Office. Print close PDF version Last update 19-10-2017 HU Credits: 4 Degree/Cycle: 2nd degree (Master) Responsible Department: mathematics Semester: 2nd Semester Teaching Languages: Hebrew Campus: E. Safra Course/Module Coordinator: Prof Ehud de Shalit Coordinator Email: rlivne@math.huji.ac.il Coordinator Office Hours: by appointment Teaching Staff: Prof Ehud Deshalit Course/Module description: Elliptic functions; the Abel-Jacobi theorem; theta functions; elliptic curves as Riemann surfaces; the embedding into P^2;the Eisenstein series;the addition law; rationality issues; the endomorphism ring;the action of SL(2,Z) on the upper half plane;modular forms;the j-function and the moduli space; cubics and elliptic curves over C; the graded ring of modular forms for SL(2,Z); multiplication by m and the associated exact sequence over C and over Q-bar; Galois cohomology; Hilbert 90; the descent exact sequence; the p-adic analog; reduction mod p; the weak Mordell-Weil theorem; heights; behaviour of heights under a map; the Mordell-Weil theorem; Course/Module aims: Acquaintance with the basic properties of elliptic curves over C and modular forms; the basic results over Q and reduction modulo p; the Mordell-Weil theorem. Learning outcomes - On successful completion of this module, students should be able to: The students will know the basic theory of elliptic functions, elliptic curves, modular forms and the connection between them; the basic facts about Galois cohomology and its use, together with algebraic geometry, to obtain Diophantine results. Attendance requirements(%): 100% Teaching arrangement and method of instruction: frontal lectures. Assignment of exercises Course/Module Content: See above Required Reading: None Additional Reading Material: Course/Module evaluation: End of year written/oral examination 100 % Presentation 0 % Participation in Tutorials 0 % Project work 0 % Assignments 0 % Reports 0 % Research project 0 % Quizzes 0 % Other 0 % Additional information: According to the number of participants and their level, there might be a take-home exam or a project work instead of a written examination in class. Print