ERC Consolidator Grant · 2020
Shimura varieties and the Birch--Swinnerton-Dyer conjecture
One of the most famous open problems in mathematics is the Birch–Swinnerton-Dyer (BSD) conjecture, which predicts that the size of the set of rational points on an elliptic curve is determined by the order of vanishing at s = 1 of its Hasse–Weil L-function. Building a crucial breakthrough due to Kolyvagin in the 1990's—the discovery of the first example of an "Euler system"—the BSD conjecture has now been proved for a wide class of elliptic curves over the rationals: those where the order of vanishing of the L-function (the "analytic rank") is 0 or 1, which conjecturally accounts for 100% of elliptic curves. However, the case of elliptic curves over the rationals is only the tip of an…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.