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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Any Farey triangle corresponds to a variant of the Colmez-Fontaine fundamental lemma, with the original lemma matching the triangle (1/0, 1/1, 0/1).
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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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Modular variants of p-adic fundamental sequence
Any Farey triangle corresponds to a variant of the Colmez-Fontaine fundamental lemma, with the original lemma matching the triangle (1/0, 1/1, 0/1).