## Jochen Heinloth - Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves

epiga:2062 - Épijournal de Géométrie Algébrique, January 15, 2018, Volume 1 - https://doi.org/10.46298/epiga.2018.volume1.2062
Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves

Authors: Jochen Heinloth

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.

Volume: Volume 1
Published on: January 15, 2018
Accepted on: January 15, 2018
Submitted on: July 23, 2017
Keywords: Mathematics - Algebraic Geometry