A support theorem for the Hitchin fibration: The case of SLn

Mark Andrea De Cataldo

doi:10.1112/S0010437X17007096

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

Mark Andrea De Cataldo

Mathematics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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 Chaudouard and Laumon. Along the way, we prove that the Tate module of the relative Prym group scheme is polarizable, and we also prove δ-regularity results for some auxiliary weak abelian fibrations.

Original language	English
Pages (from-to)	1316-1347
Number of pages	32
Journal	Compositio Mathematica
Volume	153
Issue number	6
DOIs	https://doi.org/10.1112/S0010437X17007096
State	Published - Jun 1 2017

Keywords

Hitchin morphism
decomposition theorem
special linear group
supports

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abstract = "We prove that the direct image complex for the D-twisted SLn Hitchin fibration is determined by its restriction to the elliptic locus, where the spectral curves are integral. The analogous result for GLn 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 δ-regularity results for some auxiliary weak abelian fibrations.",

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KW - decomposition theorem

KW - special linear group

KW - supports

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

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Keywords

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