  We extend the short presentation due to [Borel '53] of the cohomology ring of
a generalized flag manifold to a relatively short presentation of the
cohomology of any of its Schubert varieties. Our result is stated in a
root-system uniform manner by introducing the essential set of a Coxeter group
element, generalizing and giving a new characterization of [Fulton '92]'s
definition for permutations. Further refinements are obtained in type A.
