Derived functors and sheaf cohomology:
"The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sh...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
[2020]
|
| Schriftenreihe: | Contemporary mathematics and its applications : monographs, expositions and lecture notes
v. 2 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra. The first part of the book provides the foundational material: Chapter 1 deals with category theory and homological algebra. Chapter 2 is devoted to the development of the theory of derived functors, based on the notion of injective object. In particular, the universal properties of derived functors is stressed, with a view to make the proofs in the following chapters as simple and natural as possible. Chapter 3 provides a rather thorough introduction to sheaves, in a general topological setting. Chapter 4 introduces sheaf cohomology as a derived functor, and, after also defining Čech cohomology, develops a careful comparison between the two cohomologies which is a detailed analysis not easily available in the literature. This comparison is made using general, universal properties of derived functors. This chapter also establishes the relations with the de Rham and Dolbeault cohomologies. Chapter 5 offers a friendly approach to the rather intricate theory of spectral sequences by means of the theory of derived triangles, which is precise and relatively easy to grasp. It also includes several examples of specific spectral sequences. Readers will find exercises throughout the text, with additional exercises included at the end of each chapter"--Publisher's website |
| Beschreibung: | 1 Online-Ressource (xiii, 199 Seiten) |
| ISBN: | 9789811207297 9811207291 |
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| 520 | |a "The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra. The first part of the book provides the foundational material: Chapter 1 deals with category theory and homological algebra. Chapter 2 is devoted to the development of the theory of derived functors, based on the notion of injective object. In particular, the universal properties of derived functors is stressed, with a view to make the proofs in the following chapters as simple and natural as possible. Chapter 3 provides a rather thorough introduction to sheaves, in a general topological setting. Chapter 4 introduces sheaf cohomology as a derived functor, and, after also defining Čech cohomology, develops a careful comparison between the two cohomologies which is a detailed analysis not easily available in the literature. This comparison is made using general, universal properties of derived functors. This chapter also establishes the relations with the de Rham and Dolbeault cohomologies. Chapter 5 offers a friendly approach to the rather intricate theory of spectral sequences by means of the theory of derived triangles, which is precise and relatively easy to grasp. It also includes several examples of specific spectral sequences. Readers will find exercises throughout the text, with additional exercises included at the end of each chapter"--Publisher's website | ||
| 650 | 4 | |a Functor theory | |
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| author_facet | Bruzzo, U. |
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| bvnumber | BV047124205 |
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| ctrlnum | (ZDB-124-WOP)00011473 (OCoLC)1237585149 (DE-599)BVBBV047124205 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-search | 514/.23 |
| dewey-sort | 3514 223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV047124205 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:30:24Z |
| indexdate | 2024-07-10T09:03:18Z |
| institution | BVB |
| isbn | 9789811207297 9811207291 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032530445 |
| oclc_num | 1237585149 |
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| physical | 1 Online-Ressource (xiii, 199 Seiten) |
| psigel | ZDB-124-WOP |
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| publisher | World Scientific |
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| series2 | Contemporary mathematics and its applications : monographs, expositions and lecture notes |
| spelling | Bruzzo, U. Verfasser aut Derived functors and sheaf cohomology by Ugo Bruzzo, Beatriz Graña Otero Singapore World Scientific [2020] 1 Online-Ressource (xiii, 199 Seiten) txt rdacontent c rdamedia cr rdacarrier Contemporary mathematics and its applications : monographs, expositions and lecture notes v. 2 "The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra. The first part of the book provides the foundational material: Chapter 1 deals with category theory and homological algebra. Chapter 2 is devoted to the development of the theory of derived functors, based on the notion of injective object. In particular, the universal properties of derived functors is stressed, with a view to make the proofs in the following chapters as simple and natural as possible. Chapter 3 provides a rather thorough introduction to sheaves, in a general topological setting. Chapter 4 introduces sheaf cohomology as a derived functor, and, after also defining Čech cohomology, develops a careful comparison between the two cohomologies which is a detailed analysis not easily available in the literature. This comparison is made using general, universal properties of derived functors. This chapter also establishes the relations with the de Rham and Dolbeault cohomologies. Chapter 5 offers a friendly approach to the rather intricate theory of spectral sequences by means of the theory of derived triangles, which is precise and relatively easy to grasp. It also includes several examples of specific spectral sequences. Readers will find exercises throughout the text, with additional exercises included at the end of each chapter"--Publisher's website Functor theory Sheaf theory Spectral sequences (Mathematics) Graña Otero, Beatriz Sonstige oth https://www.worldscientific.com/worldscibooks/10.1142/11473#t=toc Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Bruzzo, U. Derived functors and sheaf cohomology Functor theory Sheaf theory Spectral sequences (Mathematics) |
| title | Derived functors and sheaf cohomology |
| title_auth | Derived functors and sheaf cohomology |
| title_exact_search | Derived functors and sheaf cohomology |
| title_exact_search_txtP | Derived functors and sheaf cohomology |
| title_full | Derived functors and sheaf cohomology by Ugo Bruzzo, Beatriz Graña Otero |
| title_fullStr | Derived functors and sheaf cohomology by Ugo Bruzzo, Beatriz Graña Otero |
| title_full_unstemmed | Derived functors and sheaf cohomology by Ugo Bruzzo, Beatriz Graña Otero |
| title_short | Derived functors and sheaf cohomology |
| title_sort | derived functors and sheaf cohomology |
| topic | Functor theory Sheaf theory Spectral sequences (Mathematics) |
| topic_facet | Functor theory Sheaf theory Spectral sequences (Mathematics) |
| url | https://www.worldscientific.com/worldscibooks/10.1142/11473#t=toc |
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