When: Nov. 14th. 2019 (Thurs), 16:00--17:15.

Where: Bldg.110, Rm. N103.

Speaker: Dohyeong Kim, Seoul National University.

Title: Arithmetic of curves and L-functions

Abstract: We will recall the quadratic reciprocity law of Euler and Gauss. It is a prototype for later reciprocity laws. In particular, it will be compared to the law for elliptic curves defined over the rationals. The latter is also known as the modularity theorem. We will see how the modularity allows us to define certain analytic invariant and a toy case of the Birch and Swinnerton-Dyer conjecture will be introduced. The guiding principles of Birch and Swinnerton-Dyer have been realized using Iwasawa theory, in which both complex analytic and p-adic analytic invariants are compared to arithmetic ones attached to Selmer groups. Hyperbolic curves are handled by generalizing Selmer groups to Selmer varieties. The study of the latter interacts strongly with Iwasawa theory.

Where: Bldg.110, Rm. N103.

Speaker: Dohyeong Kim, Seoul National University.

Title: Arithmetic of curves and L-functions

Abstract: We will recall the quadratic reciprocity law of Euler and Gauss. It is a prototype for later reciprocity laws. In particular, it will be compared to the law for elliptic curves defined over the rationals. The latter is also known as the modularity theorem. We will see how the modularity allows us to define certain analytic invariant and a toy case of the Birch and Swinnerton-Dyer conjecture will be introduced. The guiding principles of Birch and Swinnerton-Dyer have been realized using Iwasawa theory, in which both complex analytic and p-adic analytic invariants are compared to arithmetic ones attached to Selmer groups. Hyperbolic curves are handled by generalizing Selmer groups to Selmer varieties. The study of the latter interacts strongly with Iwasawa theory.