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rank of a coherent sheaf

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Topos Theory

topos theory

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In higher category theory

Theorems

Homological algebra

homological algebra

(also nonabelian homological algebra)

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Homology theories

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Contents

Idea

As the concept of coherent sheaf is a generalization of that of (complex, algebraic vector bundle) vector bundle, the concept of rank of a coherent sheaf is the corresponding generalization of that of rank of a vector bundle.

Definition

e.g. (Huybrechts-Lehn 96, def. 1.2.2)

References

This appeared in the Grothendieck’s FGA in order to treat the moduli problems leading to Quot schemes. See Nitsure’s contribution at FGA explained for a modern remake.

Last revised on October 3, 2018 at 10:20:46. See the history of this page for a list of all contributions to it.