Multiplicativity of the perverse filtration in the $\mathrm{SL}_n$ case

Source abstract

We prove that the perverse filtration of the canonical $\mathrm{SL}_n$ Hitchin system is multiplicative when the rank and degree are coprime. Over the elliptic locus of an even-degree twisted Hitchin system, we compare the Fourier projectors for compactified Pryms with the endoscopic correspondence. We then use the square-zero property of the variant cohomology and a parabolic Higgs moduli reduction to pass to the full canonical moduli space.