18.782 - Arithmetic Geometry


Course outline

A tentative schedule and list of planned topics is available here here.

Text Book

There is no required text; lecture notes will be provided. We may make reference to material in the following books and online resources (others may be added as we go along). Additional readings relevant to particular lectures will be posted on the Lectures page.

    Algebraic curves: an introduction to algebraic geometry, William Fulton.

    Elliptic curves, J.S. Milne.

    A course in arithmetic, Jean-Pierre Serre.

    Basic algebraic geometry I: varieties in projective space, 3rd edition, Igor Shafarevich.

    Algebraic function fields and codes, 2nd edition, Henning Stichtenoth.

    The arithmetic of elliptic curves, 2nd edition, Joseph H. Silverman. (errata)


Some of the theorems presented in lecture will be demonstrated using the Sage computer algebra system. Students will be provided with access to a Sage notebook server, which may be of assistance in solving some of the homework problems. Other computer algebra packages such as Magma, Maple, Matlab, and Mathematica are also available to those who wish to use them.

Problem Sets

There will be weekly problem sets.

Problem sets are to be prepared in typeset form (typically via latex) and submitted electronically in pdf format. Collaboration is permitted/encouraged, but you should first attempt to solve the problems on your own, and in any case, you must write up your own solutions. Any collaborators should be identified, as well as any resources you consulted that are not listed above or on the lectures page.


Your grade will be determined by your average problem set score, after dropping your lowest score. There are no exams and no final.