Indecomposable quadratic lattices over global function fields

In this paper, we prove that there exists an indecomposable lattice of rank 5 over a Hasse domain of any rational function field in which −1 is not a square, which solves a problem proposed by Gerstein. We also construct three concrete indecomposable lattices of rank 6 and rank 5 over a Hasse domain of the rational function field F7(x)F7(x).