The Fourier Transform and Characteristic Cycles of Monodromic $\mathrm{\ell }$-adic Sheaves

Brylinski and Malgrange proved in 1986 that, for a monodromic algebraic D-module on a finite dimensional vector space over the complex numbers, its characteristic cycle is canonically identified with the characteristic cycle of its Fourier transform. We prove the exact analogue of this in the $\mathrm{\ell }$-adic context.