A fractional version of Rivière's GL(n)-gauge.

We prove that for antisymmetric vector field Ω with small L 2 -norm there exists a gauge A ∈ L ∞ ∩ W ˙ 1 / 2 , 2 (R 1 , G L (N)) such that div 1 2 (A Ω - d 1 2 A) = 0. This extends a celebrated theorem by Rivière to the nonlocal case and provides conservation laws for a class of nonlocal equations with antisymmetric potentials, as well as stability under weak convergence. [ABSTRACT FROM AUTHOR]