Derived Category Methods in Commutative Algebra (交換代數中的導出類別方法)

Christensen, Lars Winther, Foxby, Hans-Bjørn, Holm, Henrik

Derived Category Methods in Commutative Algebra
  • 出版商: Springer
  • 出版日期: 2024-12-05
  • 售價: $9,740
  • 貴賓價: 9.5 折 $9,253
  • 語言: 英文
  • 頁數: 1131
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031774523
  • ISBN-13: 9783031774522

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendieck's Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to expand.

This book guides readers familiar with rings and modules through the construction of the associated derived category and its triangulated functors. In this context, it develops theories of categorical equivalences for subcategories and homological invariants of objects. The second half of the book focuses on applications to commutative Noetherian rings.

The book can be used as a text for graduate courses, both introductory and advanced, and is intended to serve as a reference for researchers in commutative algebra and related fields. To accommodate readers new to homological algebra, it offers a significantly higher level of detail than most existing texts on the subject.

商品描述(中文翻譯)

衍生類別方法在1960年代後半期進入了交換代數領域，提供了包括對Grothendieck的局部對偶定理的清晰表述框架在內的多種貢獻。自那時以來，它們對該領域的影響穩步增長，並持續擴展。

本書引導熟悉環和模的讀者構建相關的衍生類別及其三角函子。在這個背景下，發展了子類別的類別等價理論和對象的同調不變量。書的後半部分專注於對交換Noetherian環的應用。

本書可作為研究生課程的教材，無論是入門還是進階，並旨在為交換代數及相關領域的研究人員提供參考。為了照顧對同調代數不熟悉的讀者，本書提供了比大多數現有教材更高的細節水平。

作者簡介

Lars Winther Christensen is since 2016 Professor of Mathematics at Texas Tech University. He received his Ph.D. from the University of Copenhagen in 1999 under the direction of Hans-Bjørn Foxby. He is the author of more than 50 research articles and book chapters and maintains active research programs in commutative algebra and homological algebra of rings. His first book was Gorenstein Dimensions (2000).

Hans-Bjørn Foxby (1947-2014) was appointed Associate Professor of Mathematics at the University of Copenhagen in 1975 and promoted to Docent in 1988. He received his Ph.D. in 1973 from the same institution under the direction of Christian U. Jensen. He published more than 30 highly influential research papers and is known for his contributions to commutative algebra.

Henrik Holm is since 2011 Associate Professor of Mathematics at the University of Copenhagen. He received his Ph.D. in 2004 from the same institution under the direction of Hans-Bjørn Foxby. He has published more than 30 research papers in homological algebra, ring theory, and category theory and is known for his contributions to Gorenstein homological algebra.

作者簡介(中文翻譯)

Lars Winther Christensen 自2016年起擔任德州科技大學數學教授。他於1999年在哥本哈根大學獲得博士學位，指導教授為 Hans-Bjørn Foxby。他是超過50篇研究文章和書籍章節的作者，並在交換代數和環的同調代數方面維持活躍的研究計畫。他的第一本書是《Gorenstein Dimensions》（2000年）。

Hans-Bjørn Foxby（1947-2014）於1975年被任命為哥本哈根大學數學副教授，並於1988年晉升為Docent。他於1973年在同一機構獲得博士學位，指導教授為 Christian U. Jensen。他發表了超過30篇具有高度影響力的研究論文，並因其對交換代數的貢獻而聞名。

Henrik Holm 自2011年起擔任哥本哈根大學數學副教授。他於2004年在同一機構獲得博士學位，指導教授為 Hans-Bjørn Foxby。他在同調代數、環論和範疇論方面發表了超過30篇研究論文，並因其對 Gorenstein 同調代數的貢獻而聞名。

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