MARC details
| 000 -LEADER |
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| fixed length control field |
02441 a2200229 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
AT-ISTA |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20240109104534.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
240109s2023 |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783658430306 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
Institute of Science and Technology Austria (ISTA) |
| Transcribing agency |
Institute of Science and Technology Austria (ISTA) |
| 041 ## - LANGUAGE CODE |
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| Language code of text/sound track or separate title |
eng |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Edition number |
23 |
| Classification number |
516 |
| 100 10 - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Görtz, Ulrich |
| 9 (RLIN) |
972635 |
| Relator code |
aut |
| 245 ## - TITLE STATEMENT |
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| Title |
Algebraic Geometry II: |
| Remainder of title |
Cohomology of Schemes ; with examples and exercises |
| Statement of responsibility, etc. |
Ulrich Görtz, Torsten Wedhorn |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc. |
Wiesbaden |
| Name of publisher, distributor, etc. |
Springer Spektrum |
| Date of publication, distribution, etc. |
[2023] |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
VII, 869 pages |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Springer Studium Mathematik - Master |
| International Standard Serial Number |
2509-9310 |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Introduction.- 17 Differentials.- 18 Étale and smooth morphisms.- 19 Local complete intersections.- 20 The étale topology.- 21 Cohomology of sheaves of modules.- 22 Cohomology of quasi-coherent modules.- 23 Cohomology of projective and proper schemes.- 24 Theorem on formal functions.- 25 Duality.- 26 Curves.- 27 Abelian schemes.- F Homological algebra.- G Commutative algebra II. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes.<br/>It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously.<br/><br/>The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results. |
| 700 10 - ADDED ENTRY--PERSONAL NAME |
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| Relator code |
aut |
| Personal name |
Wedhorn, Torsten |
| 9 (RLIN) |
972102 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |