On some arithmetic of Satge curves

Abstract: Let n>2 be a cube free integer, we consider the elliptic curves of the form C_n: x^3+y^3=n. In this talk, we will prove that the 3-part of BSD conjecture for C_2p (resp. C_2p^2), where p ≡ 2 (resp. 5) mod 9 is an odd prime. The 2-part of the Tate-Shafarevich group of those curves will also be discussed. This is joint work with Y.Kezuka.

number theory

Audience: researchers in the topic

Algebra and Number Theory Seminars at Université Laval