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.