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Distinguishing Algebraic Spaces from Schemes

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arxiv 2411.07169 v1 pith:QVNVFPE2 submitted 2024-11-11 math.AG

Andres Fernandez Herrero , Dario Wei{ss}mann , Xucheng Zhang This is my paper · ORCID
classification math.AG
keywords algebraicinvariantsmodulischemespacesapplicationbundlescriteria
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We introduce local invariants of algebraic spaces and stacks which measure how far they are from being a scheme. Using these invariants, we develop mostly topological criteria to determine when the moduli space of a stack is a scheme. As an application we study moduli of principal bundles on a smooth projective curve.

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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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