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Titlebook: Introduction to Algebraic Geometry; Igor Kriz,Sophie Kriz Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusive l

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发表于 2025-3-21 18:38:08 | 显示全部楼层 |阅读模式
书目名称Introduction to Algebraic Geometry
编辑Igor Kriz,Sophie Kriz
视频video
概述Explains the motivations behind concepts as they arise, often comparing them to their counterparts in other areas of mathematics.Includes foundational concepts from commutative algebra and details the
图书封面Titlebook: Introduction to Algebraic Geometry;  Igor Kriz,Sophie Kriz Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusive l
描述.The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained. .The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry..
出版日期Textbook 2021
关键词algebraic variety; scheme; commutative algebra; crystalline and motivic cohomology; geometry
版次1
doihttps://doi.org/10.1007/978-3-030-62644-0
isbn_softcover978-3-030-62643-3
isbn_ebook978-3-030-62644-0
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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发表于 2025-3-21 20:54:45 | 显示全部楼层
Igor Kriz,Sophie KrizExplains the motivations behind concepts as they arise, often comparing them to their counterparts in other areas of mathematics.Includes foundational concepts from commutative algebra and details the
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https://doi.org/10.1007/978-3-030-62644-0algebraic variety; scheme; commutative algebra; crystalline and motivic cohomology; geometry
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发表于 2025-3-22 14:18:31 | 显示全部楼层
Properties of Schemes,It is immediately apparent from the definition, and the basic examples we studied, that the concept of a scheme is far more general than the concept of a variety as introduced in Chap. ., just as a topological space is much more general than a subset of .. What are the properties of schemes we should study?
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Sheaves of Modules,spond, for Noetherian schemes, to closed subschemes. A particularly important application of sheaves of ideals is the theory of ., a construction which allows us, for example, to replace a point with a subscheme of codimension 1, while not disturbing (and, in fact, often even improving) smoothness.
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