A support theorem for the Hitchin fibration: the case of $\text{SL}_{n}$. (26th April 2017)

• Record Type: Journal Article
• Authors: de Cataldo, Mark Andrea
• Is Part Of: Compositio mathematica. Volume 153:Number 6(2017)
• Page Start: 1316
• Page End: 1347
• Publication Date: 2017-04-26
• Subjects: 14D20, -- 14H60 (primary); Hitchin morphism, -- special linear group, -- decomposition theorem, -- supports; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X17007096
• Languages: English
• ISSNs: 0010-437X

Abstract

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.