On the BSD Conjecture and Recent Developments

Course Description and Grading Breakdown
We plan to discuss some of the recent and ongoing developments in the arithmetic of elliptic curves over the rationals, especially in regards to the Birch and Swinnerton-Dyer conjecture. The developments rely on an intriguing mix of techniques arising from Iwasawa theory, congruences between modular forms, the theory of Beilinson--Kato elements and Heegner points, along with related Euler systems. We hope to survey some of the underlying ideas.    Prerequisites are some background in algebraic geometry (Ma130) and algebraic number theory (Ma160). 

Course Meeting Time and Location
Tuesday and Thursday
10:30 - 11:55 am
387 Linde

Course Instructor Contact Information and Office Hours
258 Linde Hall

Course Schedule and Textbook


Course Policies
Late work - 

 Date PostedAssignment Due Date 

Midterm and Final Exam

Collaboration Table
You may consult:  
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
Your notes (taken in class)YESYES
Class notes of othersYESNO
Your hand copies of class notes of othersYESYES
Photocopies of class notes of othersYESNO
Electronic copies of class notes of othersYESNO
Course handoutsYESYES
Your returned homework / examsYESYES
Solutions to homework / exams (posted on webpage)YESYES
Homework / exams of previous yearsNONO
Solutions to homework / exams of previous yearsNONO
Emails from TAsYESNO
You may:

Discuss problems with othersYESNO
Look at communal materials while writing up solutionsYESNO
Look at individual written work of othersNONO
Post about problems onlineNONO
For computational aids, you may use:


* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.