Any order over a reduced separated finite type scheme over a char 0 field can be resolved by an Azumaya algebra over a smooth DM stack via a sequence of stacky blow-ups.
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Generalizes Etingof-Eu graded Euler characteristic approach to higher preprojective algebras and shows that for 2-representation finite algebras from type A tensor products, the full graded Hochschild (co)homology and cyclic homology follow from the center and HH_0.
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The Azumification of orders
Any order over a reduced separated finite type scheme over a char 0 field can be resolved by an Azumaya algebra over a smooth DM stack via a sequence of stacky blow-ups.
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Hochschild (co)homology and cyclic homology via a graded Euler characteristic with applications to higher preprojective algebras
Generalizes Etingof-Eu graded Euler characteristic approach to higher preprojective algebras and shows that for 2-representation finite algebras from type A tensor products, the full graded Hochschild (co)homology and cyclic homology follow from the center and HH_0.