Extending Elliptic Curve Chabauty to higher genus curves

We give a generalization of the method of "Elliptic Curve Chabauty" to higher genus curves and their Jacobians. This method can sometimes be used in conjunction with covering techniques and a modified version of the Mordell-Weil sieve to provide a complete solution to the problem of determining the set of rational points on an algebraic curve Y. We show how to apply these explicitly by using them to prove that the equation y (2) = (x (3) + x (2) - 1) I broken vertical bar(11)(x) has no rational solutions.