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概型的几何
《概型的几何(英文版)》内容简介:概型理论是代数几何的基础,在代数几何的经典领域不变理论和曲线模中有了较好的发展。将代数数论和代数几何有机的结合起来,实现了早期数论学者们的愿望。这种结合使得数论中的一些主要猜测得以证明。 《概型的几何(英文版)》旨在建立起经典代数几何基本教程和概型理论之间的桥梁。例子讲解详实,努力挖掘定义背后的深层次东西。练习加深读者对内容的理解。学习《概型的几何(英文版)》的起点低,了解交换代数和代数变量的基本知识即可。《概型的几何(英文版)》揭示了概型和其他几何观点,如流形理论的联系。了解这些观点对学习《概型的几何(英文版)》是相当有益的,虽然不是必要。目次:基本定义;例子;射影概型;经典结构;局部结构;概型和函子。 -
大学代数几何
《大学代数几何(英文版)》内容为:There are several good recent textbooks on algebraic geometry atthe graduate level.but not(to my knowledge)any designed for anundergraduate course.Humble notes are from a course given in twosuccessive years in the 3rd year of the Warwick undergraduate mathcourse,and are intended as a self-contained introductory textbook. -
Etale Cohomology Theory
Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra. -
Basic algebraic geometry 1
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Complex Algebraic Surfaces
Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor Beauville gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research. -
Elements de Geometrie Algebrique I