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arXiv · 2211.09630

The de Rham stack and the variety of very good splittings of a curve

Mark Andrea A. de Cataldo·Michael Groechenig·Siqing Zhang
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Abstract

The stack of relative splittings of a special Azumaya algebra plays a key role in the Non-Abelian Hodge Theory for curves in positive characteristics. In this paper, we define and study an open substack consisting of the so-called very good splittings. We show that, when using very good splittings, the Non-Abelian Hodge isomorphism preserves the semistable loci on the Dolbeault and the de Rham sides. We also show that the stack of very good splittings admits a quasi-projective tame moduli space. As a consequence, we show that the derived pushforwards of the intersection complexes by the Hitchin and the de Rham-Hitchin morphisms are isomorphic and they have isomorphic perverse cohomology sheaves.

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Mark Andrea A. de Cataldo, Michael Groechenig, Siqing Zhang. 2023-06-14. The de Rham stack and the variety of very good splittings of a curve. https://doi.org/10.4310/mrl.241211041444

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