CRM-ISM-AMQ 2023 Prize awarded to Ashay Burungale, Francesc Castella, Christopher Skinner and Ye Tian

The 2023 CRM-ISM-AMQ Prize is awarded  to Ashay Burungale (UT Austin), Francesc Castella (UCSB), Christopher Skinner (Princeton) and Ye Tian (University of Chinese Academy of Sciences) for their article “p∞-Selmer groups and rational points on CM elliptic curve”, published in the special issue of Annales Mathématiques du Québec in honour of Bernadette Perrin-Riou.

In recent years, an important breakthrough in the study of the Birch and Swinnerton-Dyer conjecture is the so-called p-converse theorem pioneered by Chris Skinner. The BSD conjecture predicts that the algebraic and analytic ranks of an elliptic curve are equal. The p-converse theorem states that if the algebraic rank given by the Selmer group of an elliptic curve is 1, then the analytic rank is 1, which proves the BSD conjecture for a large family of elliptic curves. The article studies a new method that generalizes previous results to a number of new settings. It is also the building block of further generalizations to totally real fields announced by the authors. This article can be an important steppingstone for many further results in the study of the BSD conjecture.

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