Abstract

Let E be a rational elliptic curve with good supersingular reduction at an odd prime p with a_p=0. In this talk, we will show that the characteristic power series of Kobayashi's signed Selmer groups attached to E satisfy a p-adic analogue of the Birch—Swinnerton-Dyer conjecture. In rank 0, this gives a new proof of a result due to Byoung-Du Kim, and in positive rank, it confirms a folklore conjecture stated in a recent work of Kundu—Ray. The key ingredient in the proof is a leading term formula due to Perrin-Riou for a generator of her module of p-adic L-functions in the Dieudonné module of E. The talk is based on the PhD thesis of C. Alar.

 

Organizer: Ming-Lun Hsieh (NTU)