The Schur algebra for the general linear group has finite global dimension. So one can try to construct explicit projective resolutions of the Weyl modules for the Schur algebra. Let R be a commutative ring and denote by U^+_n(R) the Kostant form over R of the universal enveloping algebra of the Lie algebra of n x n complex nilpotent upper triangular matrices. In this talk I will explain the construction of functors that map (minimal) projective resolutions of the rank-one trivial U^+_n(R)-module to (minimal) projective resolutions of rank-one modules for the Borel-Schur algebra. Using Woodcock's Theorem, from these resolutions one can easily obtain projective resolutions of the Weyl modules for the Schur algebra. This is joint work with Ivan Yudin.