Ashay Burungale (University of Texas)

The talk plans to outline the existence of two-variable zeta element over an imaginary quadratic field for an elliptic curve defined over Q. Its arithmetic consequences include proof of Kobayashi’s main conjecture for semistable curves and special cases of the Birch–Swinnerton-Dyer conjecture. (Joint with C. Skinner, Y. Tian and X. Wan.)