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The minimal model program for arithmetic surfaces enriched by a Brauer class

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arxiv 2108.03105 v1 pith:6OQANZUB submitted 2021-08-06 math.AG math.RA

Daniel Chan , Colin Ingalls This is my paper · ORCID
classification math.AGmath.RA
keywords surfacesarithmeticbetabrauercastelnuovoclassenrichedminimal
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abstract

We examine the noncommutative minimal model program for orders on arithmetic surfaces, or equivalently, arithmetic surfaces enriched by a Brauer class $\beta$. When $\beta$ has prime index $p>5$, we show the classical theory extends with analogues of existence of terminal resolutions, Castelnuovo contraction and Zariski factorisation. We also classify $\beta$-terminal surfaces and Castelnuovo contractions, and discover new unexpected behaviour.

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  1. Some terminal orders on 3-folds

    math.AG 2026-07 accept novelty 7.0 of 10

    First non-trivial terminal local orders in dimension three are constructed as maximal orders with toric ramification data and as deformed symbols ramified on Kleinian singularities.

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