椭圆曲线算术中的高等论题

作者简介

《椭圆曲线算术中的高等论题(英文版)》内容简介：美国哈佛大学从1977年开始，曾多次举办”椭圆曲线” 班，《椭圆曲线算术中的高等论题(英文版)》作者是该讨论班成员之一。椭圆曲线是一个古老的数学课题，最近由于代数数论和代数几何等现代数学的进展，使它得到了新的活力。《椭圆曲线算术中的高等论题(英文版)》是以1986年版的《椭圆曲线的算术理论》为蓝本，但在知识体系上做了较大的改动形成了这不教程，讲述上也更加专业，但在思想上是作者前《椭圆曲线算术中的高等论题(英文版)》的延续。包括椭圆和模型函数；复乘方法；椭圆曲线；Néron模型；复域上的椭圆曲线等内容。每章末都配有大量习题。目次：椭圆和模型函数；复乘方法；椭圆曲线；Néron模型；复域上的椭圆曲线。

读者对象：适合数学专业的研究生和相关的科研人员。

书籍目录

PrerepuisitesChapter 1　The standard Brownian motionChapter 2  Brownian local timesChapter 3  The general 1-dimensional diffusionChapter 4  GeneratorsChapter 5  Time changes and killing Chapter 6  Local and inverse local timesChapter 7  Brownian motion in several dimensionsChapter 8  A general view of diffusion in several dimensionsBibliography List of notationsIndex

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《椭圆曲线算术中的高等论题(英文版)》是由世界图书出版公司出版的。

前言

In the introduction to the first volume of The Arithmetic o/Elliptic Curves（Springer-Verlag, 1986）, I observed that "the theory of elliptic curves isrich, varied, and amazingly vast," and as a consequence, "many importanttopics had to be omitted." I included a brief introduction to ten additionaltopics as an appendix to the first volume, with the tacit understanding thateventually there might be a second volume containing the details. You arenow holding that second volume. Unfortunately, it turned out that even those ten topics would not fitinto a single book, so I was forced to make some choices. The followingmaterial is covered in this book:I. Elliptic and modular functions for the full modular group.II. Elliptic curves with complex multiplication.   III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers,Tate's algorithm, and Ogg's conductor-discriminant formula.V. Tate's theory of qcurves over p-adic fields.VI. Neron's theory of canonical local height functions.So what's still missing？ First and foremost is the theory of modularcurves of higher level and the associated modular parametrizations of ellip-tic curves. There is little question that this is currently the hottest topicin the theory of elliptic curves, but any adequate treatment would seem torequire （at least） an entire book of its own. （For a nice introduction, seeKnapp [1].） Other topics that I have left out in order to keep this bookat a manageable size include the description of the image of the g-adicrepresentation attached to an elliptic curve and local and global dualitytheory. Thus, at best, this book covers approximately half of the materialdescribed in the appendix to the first volume. I apologize to those who mayfeel disappointed, either at the incompleteness or at the choice of particulartopics.

章节摘录

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图书封面

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