  We introduce a variant of the Seiberg-Witten equations, Pin^-(2)-monopole
equations, and give its applications to intersection forms with local
coefficients of 4-manifolds. The first application is an analogue of Froyshov's
results on 4-manifolds which have definite forms with local coefficients. The
second is a local coefficient version of Furuta's 10/8-inequality. As a
corollary, we construct nonsmoothable spin 4-manifolds satisfying Rohlin's
theorem and the 10/8-inequality.
