ELLIPTIC CURVES WITH p-SELMER GROWTH FOR ALL p
نویسندگان
چکیده
منابع مشابه
p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplication
The study of non-abelian fundamental groups renders it plausible that the principle of Birch and Swinnerton-Dyer, whereby non-vanishing of L-values, in some appropriate sense, accounts for the finiteness of integral points, can eventually be extended to hyperbolic curves. Here we will discuss the very simple case of a genus 1 hyperbolic curve X/Q obtained by removing the origin from an elliptic...
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Let F be a global field of characteristic p > 0, F/F a Galois extension with Gal(F/F ) ≃ Z l (for some prime l 6= p) and E/F a non-isotrivial elliptic curve. We study the behaviour of Selmer groups SelE(L)r (r any prime) as L varies through the subextensions of F via appropriate versions of Mazur’s Control Theorem. With mild hypotheses on SelE(F )r (essentially a consequence of the Birch and Sw...
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In this paper we explain how to bound the p-Selmer group of an elliptic curve over K, a number eld. Our method is an algorithm which is relatively simple to implement, although it requires data such as units and class groups from number elds of degree at most p 1. Our method is practical for p = 3 but for larger values of p becomes impractical with current computing power. In the examples we ha...
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Let E be an elliptic curve defined over Q and with complex multiplication. For a prime p of good reduction, let E be the reduction of E modulo p. We find the density of the primes p ≤ x for which E(Fp) is a cyclic group. An asymptotic formula for these primes had been obtained conditionally by J.-P. Serre in 1976, and unconditionally by Ram Murty in 1979. The aim of this paper is to give a new ...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2012
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/has030