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Overviewtale Cohomology is one of the most important methods in modern Algebraic Geometry and Number Theory. It has, in the last decades, brought fundamental new insights in arithmetic and algebraic geometric problems with many applications and many important results. The book gives a short and easy introduction into the world of Abelian Categories, Derived Functors, Grothendieck Topologies, Sheaves, General tale Cohomology, and tale Cohomology of Curves. Full Product DetailsAuthor: Gunter Tamme , M. KolsterPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 1st ed. 1994 Dimensions: Width: 15.50cm , Height: 1.00cm , Length: 23.50cm Weight: 0.454kg ISBN: 9783540571162ISBN 10: 3540571167 Pages: 186 Publication Date: 28 September 1994 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents0. Preliminaries.- 1. Abelian Categories.- (1.1) Categories and Functors.- (1.2) Additive Categories.- (1.3) Abelian Categories.- (1.4) Injective Objects.- 2. Homological Algebra in Abelian Categories.- (2.1) 3-Functors.- (2.2) Derived Functors.- (2.3) Spectral Sequences.- 3. Inductive Limits.- (3.1) Limit Functors.- (3.2) Exactness of Inductive Limits.- (3.3) Final Subcategories.- I. Topologies and Sheaves.- 1. Topologies.- (1.1) Preliminaries.- (1.2) Grothendieck's Notion of Topology.- (1.3) Examples.- 2. Abelian Presheaves on Topologies.- (2.1) The Category of Abelian Presheaves.- (2.2) ?ech-Cohomology.- (2.3) The Functors fp and fp.- 3. Abelian,Sheaves on Topologies.- (3.1) The Associated Sheaf of a Presheaf.- (3.2) The Category of Abelian Sheaves.- (3.3) Cohomology of Abelian Sheaves.- (3.4) The Spectral Sequences for ?ech Cohomology.- (3.5) Flabby Sheaves.- (3.6) The Functors fS and fs.- (3.7) The Leray Spectral Sequences.- (3.8) Localization.- (3.9) The Comparison Lemma.- (3.10) Noetherian Topologies.- (3.11) Commutation of the Functors Hq(U, *) with Pseudofiltered Inductive Limits.- II. Etale Cohomology.- 1. The Etale Site of a Scheme.- (1.1) Etale Morphisms.- (1.2) The Etale Site.- (1.3) The Relation between Etale and Zariski Cohomology.- (1.4) The Functors f* and f*.- (1.5) The Restricted Etale Site.- 2. The Case X= spec(k).- 3. Examples of Etale Sheaves.- (3.1) Representable Sheaves.- (3.2) Etale Sheaves of Ox -Modules.- (3.3) Appendix: The Big Etale Site.- 4. The Theories of Artin-Schreier and of Kummer.- (4.1) The Groups Hq(X,(Ga)x).- (4.2) The Artin-Schreier Sequence.- (4.3) The Groups Hq(X,(Gm)x).- (4.4) The Kummer Sequence.- (4.5) The Sheaf of Divisors on Xet.- 5. Stalks of Etale Sheaves.- 6. Strict Localizations.- (6.1) Henselian Rings and Strictly Local Rings.- (6.2) Strict Localization of a Scheme.- (6.3) Etale Cohomology on Projective Limits of Schemes.- (6.4) The Stalks of Rqf*(F).- 7. The Artin Spectral Sequence.- 8. The Decomposition Theorem. Relative Cohomology.- (8.1) The Decomposition Theorem.- (8.2) The functors j! and i!.- (8.3) Relative Cohomology.- 9. Torsion Sheaves, Locally Constant Sheaves, Constructible Sheaves.- (9.1) Torsion Sheaves.- (9.2) Locally Constant Sheaves.- (9.3) Constructible Sheaves.- 10. Etale Cohomology of Curves.- (10.1) Skyscraper Sheaves.- (10.2) The Cohomological Dimension of Algebraic Curves.- (10.3) The Groups Hq(X,(Gm)x) and Hq(X,(?n)x).- (10.4) The Finiteness Theorem for Constructible Sheaves.- 11. General Theorems in Etale Cohomology Theory.- (11.1) The Comparison Theorem with Classical Cohomology.- (11.2) The Cohomological Dimension of Algebraic Schemes.- (11.3) The Base Change Theorem for Proper Morphisms.- (11.4) Finiteness Theorems.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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