Seminar: Descent theory on elliptic curves.

Thời gian: 13:00 đến 16:00 Ngày 25/04/2025

Địa điểm: Phòng C102, VIASM, 157 phố Chùa Láng, Hà Nội

Báo cáo viên: Đào Văn Thịnh (Institute of Mathematics Hanoi)

Tóm tắt: Let K be a number field, and E be an elliptic curve defined over K. It is well-known that E is an algebraic group over K, and so its set of rational points, E(K), forms a group, the so-called Mordell-Weil group. By the Mordell-Weil theorem, it is a finitely generated abelian group, and one of the big questions is how to determine it (in the sense of giving generators as points in E(K) and relations). Descent is the main tool used for that, both in theory and in practice. Doing an n-descent on E means to compute the n-Selmer group Sel_n(E), which we will introduce in this talk. The talk will mainly concentrate on n=2.