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Algebraicity and smoothness of fixed point stacks

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arxiv 2205.11114 v3 pith:K6B72V6M submitted 2022-05-23 math.AG

Matthieu Romagny (IRMAR) This is my paper · ORCID
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keywords stacksaffinealgebraicityfinitelyfixedflatfunctorsgroup
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We study algebraicity and smoothness of fixed point stacks for flat group schemes which have a finite composition series whose factors are either reductive or proper, flat, finitely presented, acting on algebraic stacks with affine, finitely presented diagonal. For this, we extend some theorems of [SGA3.2] on functors of homomorphisms Hom(G, H) and functors of reductive subgroups Sub(H) for an affine, possibly non-flat group scheme H.

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  1. Hitchin fibrations are Ng\^{o} fibrations

    math.AG 2025-02 conditional novelty 7.0 of 10

    For every split reductive group G, the Hitchin fibration in the canonical and logarithmic cases is an Ngô fibration, so its direct image splits into Ngô strings.

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