(1996) Complex multiplication structure of elliptic curves. J. Number Theory 56: pp. 227-241Lenstra, HW (1996) Complex multiplication structure of elliptic curves. J. Number Theory 56: pp. 227-241H. W. Lenstra.
The purpose of this article is to explain the main ideas of the topic with neither proofs, nor historical remarks. The exposition is divided into three parts. No modular functions appear in Part I except that the values of the j-function are needed as invariants of elliptic curves. Part II...
complex multiplicationquadratic twistsLetE/Fbe an elliptic curve defined over a number fieldF. Suppose thatEhas complex multiplication overF, i.e.EndF(E)is an imaginary quadratic field. With the aid of CM theory, we find elliptic curves whose quadratic twists have a constant root number....
In the last fifteen years the Iwasawa theory has been applied with remarkable success to elliptic curves with complex multiplication. A clear yet general exposition of this theory is presented in this book. Following a chapter on formal groups and local units, the p-adic L functions of Manin-...
Complex Multiplication 作者:Reinhard Schertz 出版年:2010-6 页数:376 定价:$ 131.08 ISBN:9780521766685 豆瓣评分 目前无人评价 评价: 写笔记 写书评 加入购书单 分享到 + 加入购书单
If E does not have complex multiplication, then \mathcal {O}=\mathbb {Z}. In this case, we are almost in the setting of [13]. For this reason, we call this paper “sequences associated to curves with complex multiplication”. In any case, even when E does not have CM, Theorem 1....
Let X/C be a K3 surface with complex multiplication by the ring of integers of a CM field E. We show that X can always be defined over an Abelian extension K/E explicitly determined by the discriminant form of the lattice NS(X). We then construct a model of X over K via Galois-...
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Part of the book series:University Series in Mathematics(USMA) Accesses Citations Altmetric About this book This is a book of "impressions" of a journey through the theory of com plex algebraic curves. It is neither self-contained, balanced, nor particularly tightly organized. As with any ...
1) complex multiplication 虚数乘法 1. Whencomplex multiplication(CM) is used to create elliptic curves over F_p,the ring of complex quadratic field is only used. 利用虚数乘法(Com p lex M u ltip lication,CM)生成Fp上的椭圆曲线,通常只使用虚二次域的最大整环。