Completion, Čech and local homology and cohomology : interactions between them
著者
書誌事項
Completion, Čech and local homology and cohomology : interactions between them
(Springer monographs in mathematics)
Springer, 2019
Corr. publication
並立書誌 全1件
大学図書館所蔵 全1件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 337-340) and index
内容説明・目次
内容説明
The aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas. A basic construction is the Cech complex with respect to a system of elements and its free resolution. The study of its homology and cohomology will play a crucial role in order to understand left derived functors of completion and right derived functors of torsion. This is useful for the extension and refinement of results known for modules to unbounded complexes in the more general setting of not necessarily Noetherian rings.
The book is divided into three parts. The first one is devoted to modules, where the adic-completion functor is presented in full details with generalizations of some previous completeness criteria for modules. Part II is devoted to the study of complexes. Part III is mainly concerned with duality, starting with those between completion and torsion and leading to new aspects of various dualizing complexes.
The Appendix covers various additional and complementary aspects of the previous investigations and also provides examples showing the necessity of the assumptions.
The book is directed to readers interested in recent progress in Homological and Commutative Algebra. Necessary prerequisites include some knowledge of Commutative Algebra and a familiarity with basic Homological Algebra. The book could be used as base for seminars with graduate students interested in Homological Algebra with a view towards recent research.
目次
Part I: Modules,- 1. Preliminaries and auxiliary results.- 2. Adic topology and completion.- 3. Ext-Tor vanishing and completeness criteria.- PartII: Complexes.- 4. Homological Preliminaries.- 5. Koszul complexes, depth and codepth.- 6. Cech complexes, Cech homology and cohomology.- 7. Local cohomology and local homology.- 8. The formal power series Koszul complex.- 9. Complements and Applications.- Part III: Duality.- 10. Cech and local duality.- 11. Dualizing complexes.- 12. Local duality with dualizing complexes and other dualities.- Appendix.- References.- Notation.- Subject Index.
「Nielsen BookData」 より