Derived Functors And Sheaf Cohomology is popular PDF and ePub book, written by Ugo Bruzzo in 2020-03-10, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Derived Functors And Sheaf Cohomology can be Read Online from any device for your convenience.
Derived Functors And Sheaf Cohomology Book PDF Summary
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 are 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.
Detail Book of Derived Functors And Sheaf Cohomology PDF
- Author : Ugo Bruzzo
- Release : 10 March 2020
- Publisher : World Scientific
- ISBN : 9789811207303
- Genre : Mathematics
- Total Page : 214 pages
- Language : English
- PDF File Size : 14,6 Mb
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