A support theorem for the Hitchin fibration: the case of $\text{SL}_{n}$. (26th April 2017) - de Cataldo, Mark Andrea
Abstract : We prove that the direct image complex for the$D$ -twisted$\text{SL}_{n}$ Hitchin fibration is determined by its restriction to the elliptic locus, where the spectral curves are integral. The analogous result for$\text{GL}_{n}$ is due to Chaudouard and Laumon. Along the way, we prove that the Tate module of the relative Prym group scheme is polarizable, and we also prove$\unicode[STIX]{x1D6FF}$ -regularity results for some auxiliary weak abelian fibrations.