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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 of Coherent Sheaves

Derived Categories of Coherent Sheaves

Chapter:
(p.62) 3 Derived Categories of Coherent Sheaves
Source:
Fourier-Mukai Transforms in Algebraic Geometry
Author(s):

D. Huybrechts

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199296866.003.0003

The discussion of the previous chapter is applied to the derived category of the abelian category of coherent sheaves. The Serre functor is introduced, and particular spanning classes are constructed. The usual geometric functors, direct and inverse image, tensor product, and global sections, are derived and extended to functors between derived categories. The compatibilities between them are reviewed. The final section focuses on the Grothendieck-Verdier duality.

Keywords:   coherent sheaf, higher direct image, derived tensor product, Grothendieck-Verdier duality

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