Arithmetic of cyclotomic fields and modular symbols

任课教师 Speaker:Emmanuel Lecouturier
时间 Time: 每周二/四 13:30-15:05 2021-2-22 ~ 5-14
地点 Venue:近春园西楼第三会议室

课程描述 Description

In this course, we first study classical Iwasawa theory, which is about the relation between class group of cyclotomic fields and Lfunctions. We then study recent conjectures of Romyar Sharifi, which are in some sense a refinement of the Iwasawa main conjecture. It relates the homology of modular curves modulo some Eisenstein ideal to the arithmetic of cyclotomic fields. Many results have been proved towards this conjecture. If times permits, we will explain some of these results.

预备知识 Prerequisites

Algebraic number theory, some algebraic topology (singular homology), basic knowledge on modular forms.

参考资料 References

1. A first course in modular forms, Diamond and Shurman, Springer.
2. Cyclotomic fields and zeta values, Coates and Sujatha, Springer.
3. Modular curves and cyclotomic fields, lecture notes by Romyar Sharifi.