# Moduli of non-commutative polarized schemes

Mathematische Annalen, Nov 2017

We construct, using geometric invariant theory, a quasi-projective Deligne–Mumford stack of stable graded algebras. We also construct a derived enhancement, which classifies twisted bundles of stable graded $$A_\infty$$-algebras. The tangent complex of the derived scheme is given by graded Hochschild cohomology, which we relate to ordinary Hochschild cohomology. We obtain a version of Hilbert stability for non-commutative projective schemes.

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K. Behrend, B. Noohi. Moduli of non-commutative polarized schemes, Mathematische Annalen, 2017, 1-34, DOI: 10.1007/s00208-017-1624-1