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.
Local homology and cohomology on schemes
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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.