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)](/https/mathworld.wolfram.com/images/equations/LocallyFinitelyPresentedMorphism/Inline6.svg)
for finite 
and 
. Thus locally the algebra 
has finitely many generators and finitely many defining relations
over 
.
This property is preserved by composition of morphisms and base change. Every smooth morphism is locally finitely presented.
