Birch and Swinnerton-Dyer Conjecture

Birch and Swinnerton-Dyer Conjecture. Rank conjectures, Selmer groups, and Heegner points.

Foundations and canonical references

The standard treatments of birch and swinnerton-dyer conjecture approach the subject from complementary angles. Silverman, The Arithmetic of Elliptic Curves (2009) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.

Supporting and adjacent work

A number of supporting contributions sharpen specific aspects of birch and swinnerton-dyer conjecture or connect it to neighbouring problems. Notes on elliptic curves. II (Birch et al., 1965) contributes to this area as one of the supporting references that inform current practice.

Open methodological questions for birch and swinnerton-dyer conjecture include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.