A locally finitely presented morphism, also called a morphism locally of finite presentation, is a morphism 
of schemes such that every
point of 
has an affine scheme neighborhood
mapping into an affine scheme neighborhood 
of its image, where 
is isomorphic to ![R[x_1,...,x_n]/(f_1,...,f_m)](/images/equations/LocallyFinitelyPresentedMorphism/Inline6.svg)
for finite 
and 
.
This property is preserved by composition and base change. Every smooth morphism is locally finitely presented.
