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

Abstract: Mori's minimal model program is a major organising principle for studying and classifying varieties $X$. It has been generalised in many directions, and in this talk, we examine a ``noncommutative'' one where $X$ is enriched by a Brauer class $\beta \in K(X)$. We focus on some new results where $X$ is a surface whose residue fields are finite. When the order of $\beta$ is a prime >5, we recover most of standard surface theory including existence of terminal resolutions, Castelnuovo contraction and Zariski factorisation. However, interesting new examples of terminal singularities and Castelnuovo contractions appear, which have no characteristic zero analogue.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

The seminar takes place on Tuesdays and Thursdays via Zoom. Zoom passwords are given via mailing list on Fridays. To join the mailing list go to the website.

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Times vary to accommodate speakers time zones but times will be announced in GMT time.