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 Office Hours:
by appointment
Teaching Staff:
Prof Ehud Deshalit
Course/Module description:
Elliptic functions; the AbelJacobi 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 jfunction 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 Qbar; Galois cohomology; Hilbert 90; the descent exact sequence; the padic analog; reduction mod p; the weak MordellWeil theorem; heights; behaviour of heights under a map; the MordellWeil 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 MordellWeil 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 takehome exam or a project work instead of a written examination in class.
