- References
In algebraic geometry, the Quot scheme is a scheme parametrizing locally free sheaves on a projective scheme. More specifically, if X is a projective scheme over a Noetherian scheme S and if F is a coherent sheaf on X, then there is a scheme 
whose set of T-points 
is the set of isomorphism classes of the quotients of 
that are flat over T. The notion was introduced by Alexander Grothendieck.[1]
It is typically used to construct another scheme parametrizing geometric objects that are of interest such as a Hilbert scheme. (In fact, taking F to be the structure sheaf 
gives a Hilbert scheme.)
References
1. ^Grothendieck, Alexander. Techniques de construction et théorèmes d'existence en géométrie algébrique III : préschémas quotients. Séminaire Bourbaki, 6 (1960-1961), Exposé No. 212, 20 p.
- Nitsure, N. Construction of Hilbert and Quot schemes. Fundamental algebraic geometry: Grothendieck’s FGA explained, Mathematical Surveys and Monographs 123, American Mathematical Society 2005, 105–137.
- https://amathew.wordpress.com/2012/06/02/the-stack-of-coherent-sheaves/
1 : Algebraic geometry
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