Iwasawa theory for deformation of ordinary elliptic curves
ثبت نشده
چکیده
منابع مشابه
Algorithms for the arithmetic of elliptic curves using Iwasawa theory
We explain how to use results from Iwasawa theory to obtain information about p-parts of Tate-Shafarevich groups of specific elliptic curves over Q. Our method provides a practical way to compute #X(E/Q)(p) in many cases when traditional p-descent methods are completely impractical and also in situations where results of Kolyvagin do not apply, e.g., when the rank of the Mordell-Weil group is g...
متن کاملOn the Tate-shafarevich Group of Elliptic Curves over Q
Let E be an elliptic curve over Q. Using Iwasawa theory, we give what seems to be the first general upper bound for the order of vanishing of the p-adic L-function at s = 0, and the Zp-corank of the Tate-Shafarevich group for all sufficiently large good ordinary primes p.
متن کاملRecent Results in the GL2 Iwasawa Theory of Elliptic Curves without Complex Multiplication
Recently new results have been obtained in the GL2 Iwasawa theory of elliptic curves without complex multiplication. This article is a survey of some of those results. Mathematics Subject Classification: 11G05, 11R23
متن کاملTwo p-adic L-functions and rational points on elliptic curves with supersingular reduction
Let E be an elliptic curve over Q. We assume that E has good supersingular reduction at a prime p, and for simplicity, assume p is odd and ap = p+ 1− #E(Fp) is zero. Then, as the second author showed, the p-adic L-function Lp,α(E) of E corresponding to α = ±√−p (by Amice-Vélu and Vishik) can be written as Lp,α(E) = f log+p +g logp α by using two Iwasawa functions f and g ∈ Zp[[Gal(Q∞/Q)]] ([20]...
متن کاملLectures on the Iwasawa Theory of Elliptic Curves
These are a very preliminary (and incomplete!) version of the author’s lectures for the 2018 Arizona Winter School on Iwasawa Theory.
متن کامل