The Heart of Cohomology

verfasst von: Goro Kato

Verlag: Springer Netherlands

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

If you have not heard about cohomology, this book may be suited for you. Fundamental notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived categories are explained in elementary fashion. Applications to sheaf cohomology are given. Also cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family are provided.

Inhaltsverzeichnis

Frontmatter

1. CATEGORY

Abstract

The notion of a category is a concise concept shared among “groups and group homomorphisms”, “set and set-theoretic mappings”, “topological spaces and continuous mappings”, e t c.

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2. DERIVED FUNCTORS

Abstract

Let A be an abelian category. We will define the category Co(A) of (cochain) complexes as follows. An object in Co(A) is a sequence of objects and morphisms

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3. SPECTRAL SEQUENCES

Abstract

A spectral sequence in an abelian category A consists of doubly indexed objects of A:

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4. DERIVED CATEGORIES

Abstract

Let A be an abelian category and let Co⁺(A) be the category of bounded from below complexes as before.

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5. COHOMOLOGICAL ASPECTS OF ALGEBRAIC GEOMETRY AND ALGEBRAIC ANALYSIS

Abstract

The most fundamental object of study in Algebraic Geometry is the set of (or the number) of solutions of a system of (polynomial) equations.

Goro Kato

Backmatter

Titel: The Heart of Cohomology
verfasst von: Goro Kato
Verlag: Springer Netherlands
Electronic ISBN: 978-1-4020-5036-7
Print ISBN: 978-1-4020-5035-0
DOI: https://doi.org/10.1007/1-4020-5036-4