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Algebraicity and smoothness of fixed point stacks

· 2022 · math.AG · arXiv 2205.11114

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abstract

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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Hitchin fibrations are Ng\^{o} fibrations

math.AG · 2025-02-07 · conditional · novelty 7.0

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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  • Hitchin fibrations are Ng\^{o} fibrations math.AG · 2025-02-07 · conditional · none · ref 2005 · internal anchor

    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.