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arXiv · 1601.02589

A support theorem for the Hitchin fibration: the case of $SL_n$

Mark Andrea A. de Cataldo
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Abstract

We prove that the direct image complex for the $D$-twisted $SL_n$ Hitchin fibration is determined by its restriction to the elliptic locus, where the spectral curves are integral. The analogous result for $GL_n$ 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.

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Mark Andrea A. de Cataldo. 2016-01-11. A support theorem for the Hitchin fibration: the case of $SL_n$. https://doi.org/10.1112/s0010437x17007096

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