A support theorem for the Hitchin fibration: the case of $S{L}_n$

Abstract

We prove that the direct image complex for the $D$-twisted $S{L}_n$ Hitchin fibration is determined by its restriction to the elliptic locus, where the spectral curves are integral. The analogous result for $G{L}_n$ is due to P.-H. Chaudouard and G. Laumon. Along the way, we prove that the Tate module of the relative Prym group scheme is polarizable, and we also prove $\delta$-regularity results for some auxiliary weak abelian fibrations.

Un-necessary irreducibility hypothesis removed. Final version. To appear in comp. math

References in corpus (3)

• Fourier-Mukai and autoduality for compactified Jacobians II
• Partial Fourier--Mukai transform for integrable systems with applications to Hitchin fibration
• Fibration de Hitchin et endoscopie

Cited by in corpus (9)

• Cohomological $\chi$-independence for moduli of one-dimensional sheaves and moduli of Higgs bundles
• Higgs bundles, Lagrangians and mirror symmetry
• Branes on the singular locus of the Hitchin system via Borel and other parabolic subgroups
• Mirror symmetry for Nahm branes
• Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations
• Geometry of the logarithmic Hodge moduli space (with an Appendix joint with Siqing Zhang)
• Motivic mirror symmetry and $\chi$-independence for Higgs bundles in arbitrary characteristic
• Mirror of Orbifold Singularities in the Hitchin Fibration: the case $({\text{SL}}_n,{\text{PGL}}_n)$
• The Norm map on the compactified Jacobian, the Prym stack and Spectral data for G-Higgs pairs