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The de Rham stack and the variety of very good splittings of a curve
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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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Cited by 1 Pith paper
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Logarithmic Non-Abelian Hodge Theory for curves in prime characteristic
A logarithmic version of the characteristic-p Non-Abelian Hodge theorem, over an Artin-Schreier cover of the Hitchin base, with semistable and GL_r cohomological applications.
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