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Fourier-Mukai Transforms in Algebraic Geometry$
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D. Huybrechts

Print publication date: 2006

Print ISBN-13: 9780199296866

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199296866.001.0001

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Derived Categories: A Quick Tour

Derived Categories: A Quick Tour

Chapter:
(p.27) 2 Derived Categories: A Quick Tour
Source:
Fourier-Mukai Transforms in Algebraic Geometry
Author(s):

D. Huybrechts

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199296866.003.0002

This chapter briefly outlines the main steps in the construction of the derived category of an arbitrary abelian category. The homotopy category of complexes is considered as an intermediate step, which is then localized with respect to quasi-isomorphisms. Left and right derived functors are explained in general, and particular examples are studied in more detail. Spectral sequences are treated in a separate section.

Keywords:   homotopy category, quasi-isomorphisms, derived functors, spectral sequences

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