Topics in Number Theory
Winter Quarter 2012
Arithmetic of Curves
Meeting Time: Regularly Mondays and Wednesdays 12:00 noon to
1:50 pm in MS 5233 and some Fridays 12:00 noon to 12:50 pm in MS 5137
Lecture Starts on Friday January 13th in MS 5137
Office hours: After class meetings, from 2:00pm to 3:00pm (MW)
in my office: MS6308.
Texts: Lecture notes will be posted: The first set of lecture
Grading will be based on student presentation (and possibly homework exercises in the lecture notes, perhaps, due early-March).
No final exam is planned.
Notes (pdf file, a tentative version now posted).
As reference books,
"Geometric Modular Forms and Elliptic Curves" (World Scientific) First or Second edition, Chapters 1, 2 and 4
Topics: I would touch the following topics in this course:
- Basics of geometry of plane curves/projective curves (some knowledge of schemes is welcome but not an absolute necessity);
- Representability of Picard functor and Jacobian of semi-stable curves;
- Sketch of applications (filling in details could be topics of presentation).
- Related topics could be touched upon in Math 290B student seminar
on Mondays at 4:00pm-5:50pm in MS 5148
(students are encouraged to attend).
Good understanding of commutative and non-commutative algebra,
algebraic number theory, Category and functors to the extent covered by 210 series.