Quot scheme

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 ${\displaystyle \operatorname {Quot} _{F}(X)}$ whose set of T-points ${\displaystyle \operatorname {Quot} _{F}(X)(T)=\operatorname {Mor} _{S}(T,\operatorname {Quot} _{F}(X))}$ is the set of isomorphism classes of the quotients of ${\displaystyle F\times _{S}T}$ that are flat over T. The notion was introduced by Alexander Grothendieck.

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