NCTS/TPE Topical Course

Topics in Algebraic Geometry and Number Theory

代數幾何與數論專題

Course Information:

Instructor : Jungkai Chen陳榮凱, I-Hsun Tsai蔡宜洵, Chia-Fu Yu余家富

Place: Old Math Bldg 103

Hours: Tue.9:10-12:10

First Meeting: 2005, Feb. 22 (Tue.)

Course description:

Algebraic geometry and number theory interweave tightly in many places. Therefore, for students who are interesting in algebraic geometry and/or number theory, it’s good to learn both these two subjects. The purpose of this course is to work on some important topics which are unlikely to be covered in regular courses. Anyone who is interesting in algebraic geometry and/or number theory is welcome.

It will be a mixture of lectures and seminar.

Topics:

Derived categories

The language of moduli spaces and representable functors

Tate thesis

GL2 Hecke theory

Class field theory

Prerequisite:

Algebra and number theory.

Reference:

Gelfand, Manin, Methods of homological algebra, Springer Verlag

Eisenbud, Harris, The geometry of schemes, GTM 197, Springer Verlag

Cassels, Frolich (Ed.), Algebraic number theory, Thompson Book Company

Bump, Automorphic forms and representations, CSAM 55, Cambridge Univ. Pr.

Lang, Algebraic Number Theory, GTM 110, Springer Verlag

Neukirch, Algebraic Number Theory

Berstein, Gelbart (Ed.), An introduction to the Langland program.