rank of a coherent sheaf

(also nonabelian homological algebra)

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*.

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

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.

- Daniel Huybrechts, Manfred Lehn,
*The Geometry of the Moduli Spaces of Sheaves*, 1996 (pdf)

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