 If "M" is a finitely generated graded module and formula_93 the associated coherent sheaf the two definitions of Hilbert polynomial agree.Since the category of coherent sheaves on a projective variety formula_94 is equivalent to the category of graded-modules modulo a finite number of graded-pieces, we can use the results in the previous section to construct Hilbert polynomials of coherent sheaves.For example, a complete intersection formula_94 of multi-degree formula_96 has the resolution