We present a new algebraic algorithm for the classical problem of weighted matroid intersection. This problem generalizes numerous well-known problems, such as bipartite matching, network flow, etc. Our algorithm has running time Õ(nrω−1 W 1+ɛ) for linear matroids with n elements and rank r, where ω is the matrix multiplication exponent, and W denotes the maximum weight of any element. This algorithm is the fastest known when W is small. Our approach builds on th