The arithmetic of supersingular elliptic curves

The project aims to reveal the hidden arithmetical properties of elliptic curves, at their so-called ''''supersingular'''' primes. This has fundamental consequences both to our understanding of elliptic curve theory, and to non-commutative Iwasawa theory in general. The investigators expect to discover/develop: (i) the asymptotic behaviour of supersingular elliptic curves over p-adic Lie extensions; (ii) a deeper understanding of the infamous Birch and Swinnerton-Dyer conjecture; (iii) a numerical method of computing L-values over non-abelian field extensions. The software developed will be marketed as part of the MAGMA computer package.