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A support theorem for the Hitchin fibration: the case of
$\text{SL}_{n}$
- Part of
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- Journal:
- Compositio Mathematica / Volume 153 / Issue 6 / June 2017
- Published online by Cambridge University Press:
- 26 April 2017, pp. 1316-1347
- Print publication:
- June 2017
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- Article
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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.
