This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularization (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.

Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)

Science & Math

Liu, Qing

Mathematics

Oxford University Press

This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem) This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularization (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford. This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students.

Oxford University Press, USA

著名学者、奇葩说导师刘擎讲透西方思想 
刘擎将在这本书中为你介绍思想史上那些"有趣的灵魂"，带你领略哲学思想中的美妙景致。你将见证韦伯"祛魅世界"的理智，发现尼采身上"天才与疯子"的结合，共情阿伦特面对大屠杀和"平庸之恶"的心境......\n与闪耀的思想交个朋友，审视眼前的生活 
刘擎在你和熠熠生辉的思想家之间搭起了一座桥梁。你可以在与这些思想家"对话"的过程中，反思自己脑袋里的观念从何而来，又如何影响着你的判断与认知。你可以借由西方现代思想，更好地审视眼前的生活。\n收获独立思考的邀请函，现代生活的行动指南 
西方思想家在特定的历史环境和社会背景中，对许多人生难题发起了深入的探索： 
为什么现代人会遭遇精神危机？ 
如果人生需要面对虚无，那么我们面对它的勇气，又该去哪里找寻？ 
为什么自由也是一种沉重的负担？ 
............ 
了解西方现代思想，正是你认识现代社会的捷径，帮助你在生活的迷雾中看清真实。\n内容简介 
人生的意义，人们向往的自由和公平的价值，人类文明的复杂冲突与未来趋势......这些让你困惑的大小问题，过去也困扰过韦伯、尼采、萨特等杰出的头脑。他们尽*努力做出阐释，为后人提供了宝贵的思想标识。\n在这部讲义里，刘擎介绍了现代视域下的19位思想大家，广泛而系统地讨论工具理性的利弊，如何面对虚无主义，消费主义对人的异化，财富分配的公平正义和全球化等议题。\n思想不惑，精神明亮。你将在这19位大家的生平故事中，理解他们建构思想大厦的地基与框架。你还会在思想大厦之上，直面个人生活和社会公共领域的诸多难题，收获审慎而真诚的回答。 
作者简介 
刘擎 
著名学者。华东师范大学教授，世界政治研究中心主任。研究方向包括政治哲学、西方思想史、现当代西方思潮与国际政治问题。代表著作《纷争的年代》《悬而未决的时刻》等。自2003年起每年撰写《西方思想年度述评》，是许多学者每年的文章。

刘擎西方现代思想讲义 (Chinese Edition)

Literature & Fiction

World Literature

Shiguang

The West Since 2000 (2003-2019) (Chinese Edition)

The Contemporary World Press

What is the meaning of life? What is the value of freedom and equity that people long for? What are the complex conflict and future trend of human civilizations? These questions that may puzzle you also puzzled Weber, Nietzsche and Sartre. The philosophers made explanation with their best try, offering precious thoughts for future generations. In this lectures, Liu Qing introduces 19 thinkers in modern field of vision, which tells the pros and cons of instrumental reason, how to face nihilism, the alienation of consumerism to human beings and the fairness and justice of wealth distribution.

Lectures on Modern Western Thought (Chinese Edition)

New Star Press

This book analyzes unexpected preference query results for three problems: causality and responsibility problems, why-not and why questions, and why-few and why-many questions. Further, it refines preference queries and discusses how to modify the original preference query based on different objectives, in order to obtain satisfying results. This highly informative and carefully presented book provides valuable insights for researchers, postgraduates and practitioners with an interest in database usability. 

Preference Query Analysis and Optimization (SpringerBriefs in Computer Science)

Computers & Technology

Gao, Yunjun

Networking & Cloud Computing

Springer

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