LEADER 03912nam  22004695  450 
001 9910300134703321
005 20200630050914.0
010   $a3-319-96517-4
024 7 $a10.1007/978-3-319-96517-8
035   $a(CKB)4100000006671734
035   $a(MiAaPQ)EBC5516528
035   $a(DE-He213)978-3-319-96517-8
035   $a(PPN)230539181
035   $a(EXLCZ)994100000006671734
100   $a20180915d2018      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aCompletion, ?ech and Local Homology and Cohomology $eInteractions Between Them /$fby Peter Schenzel, Anne-Marie Simon
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (350 pages)
225 1 $aSpringer Monographs in Mathematics,$x1439-7382
311   $a3-319-96516-6 
327   $aPart 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. ?ech complexes, ?ech homology and cohomology -- 7. Local cohomology and local homology -- 8. The formal power series Koszul complex -- 9. Complements and Applications -- Part III: Duality -- 10. ?ech and local duality -- 11. Dualizing complexes -- 12. Local duality with dualizing complexes and other dualities -- Appendix -- References -- Notation -- Subject Index.
330   $aThe aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas. A basic construction is the ?ech complex with respect to a system of elements and its free resolution. The study of its homology and cohomology will play a crucial role in order to understand left derived functors of completion and right derived functors of torsion. This is useful for the extension and refinement of results known for modules to unbounded complexes in the more general setting of not necessarily Noetherian rings. The book is divided into three parts. The first one is devoted to modules, where the adic-completion functor is presented in full details with generalizations of some previous completeness criteria for modules. Part II is devoted to the study of complexes. Part III is mainly concerned with duality, starting with those between completion and torsion and leading to new aspects of various dualizing complexes. The Appendix covers various additional and complementary aspects of the previous investigations and also provides examples showing the necessity of the assumptions. The book is directed to readers interested in recent progress in Homological and Commutative Algebra. Necessary prerequisites include some knowledge of Commutative Algebra and a familiarity with basic Homological Algebra. The book could be used as base for seminars with graduate students interested in Homological Algebra with a view towards recent research.
410  0$aSpringer Monographs in Mathematics,$x1439-7382
606   $aCommutative algebra
606   $aCommutative rings
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
615  0$aCommutative algebra.
615  0$aCommutative rings.
615 14$aCommutative Rings and Algebras.
676   $a512.24
700   $aSchenzel$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut$058453
702   $aSimon$b Anne-Marie$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910300134703321
996   $aCompletion, ?ech and Local Homology and Cohomology$91984174
997   $aUNINA