Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves
Épijournal de Géométrie Algébrique, Tome 1 (2017)
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In these notes we reformulate the classical Hilbert-Mumford criterion for GIT stability in terms of algebraic stacks, this was independently done by Halpern-Leinster. We also give a geometric condition that guarantees the existence of separated coarse moduli spaces for the substack of stable objects. This is then applied to construct coarse moduli spaces for torsors under parahoric group schemes over curves.
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author = {Heinloth, Jochen},
title = {Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves},
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Heinloth, Jochen. Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves. Épijournal de Géométrie Algébrique, Tome 1 (2017). doi: 10.46298/epiga.2018.volume1.2062
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