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Derived categories in algebraic geometry

Tác giả: Yujiro Kawamata ,
Loại tài liệu: Sách, chuyên khảo, tuyển tập
Ký hiệu: Lv7316
Mã giá: 14KA
Nội dung tóm tắt: Xem chi tiết
The study of derived categories is a subject that attracts increasingly many young mathematicians from various fields of mathematics, including abstract algebra, algebraic geometry, representation theory and mathematical physics. The concept of the derived category of sheaves was invented by Grothendieck and Verdier in the 1960s as a tool to express important results in algebraic geometry such as the duality theorem. In the 1970s, Beilinson, Gelfand and Gelfand discovered that a derived category of an algebraic variety may be equivalent to that of a finite dimensional non-commutative algebra, and Mukai found that there are non-isomorphic algebraic varieties that have equivalent derived categories. In this way the derived category provides a new concept that has many incarnations. In the 1990s, Bondal and Orlov uncovered an unexpected parallelism between derived categories and birational geometry. Kontsevich’s homological mirror symmetry provided further motivation for the study of derived categories. This book is the proceedings of a conference held at the University of Tokyo in January 2011 on the current status of the research on derived categories related to algebraic geometry. Most articles are survey papers on this rapidly developing field. The book is suitable for young mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed.
Mục lục: Xem chi tiết
Alberto Canonaco and Paolo Stellari, Fourier-Mukai functors: a survey” Sabin Cautis, Flops and about: a guide” Akira Ishii and Kazushi Ueda, A note on derived categories of Fermat varieties” Dmitry Kaledin D. B. Kaledin, Homology of infinite loop spaces” Bernhard Keller, Cluster algebras and derived categories” Izuru Mori, Some derived equivalences between noncommutative schemes and algebras” Alexander Polishchuk, Lagrangian-invariant sheaves and functors for abelian varieties”, Mihnea Popa, Generic vanishing filtrations and perverse objects in derived categories of coherent sheaves” Christian Schnell, The fundamental group is not a derived invariant” Yukinobu Toda, Introduction and open problems of Donaldson-Thomas theory” Michel Van den Bergh, Notes on formal deformations of abelian categories”

Thông tin chi tiết

    Dạng tài liệu:Bản in
    Chỉ số ISBN: 978-3-03719-115-6,
    Nguồn: Tặng biếu : Prof. Phan Thành An tặng
    Ngôn ngữ: Eng
    Mã giá: 14KA
    Mã MSC:14-06 , 14F05
    Tác giả:Yujiro Kawamata,
    Nhan đề:Derived categories in algebraic geometry
    Xuất bản, phát hành:Zürich : EMS , 2012
    Số trang:352
    Từ Khóa:derived categories
    Bộ sách:EMS Series of Congress Reports

Thông tin xếp giá

  • ĐKCB: Lv7316
  • Tổng số bản: 1
  • Tổng số bản rỗi: 0
  • Tổng số đang đặt chỗ: 0

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