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.
Theorie homotopique des DG-categories
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In this thesis we present several original contributions to the study of: - DG categories and their invariants; - Neeman's well-generated (algebraic) triangulated categories; - Fomin-Zelevinsky's cluster algebras approach via representation theory.
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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.