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SUMMARY:Daniel Chan (UNSW Sydney)
DTSTART:20220512T210000Z
DTEND:20220512T220000Z
DTSTAMP:20260423T021445Z
UID:ZAG/210
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/210/">Th
 e minimal model program for arithmetic surfaces enriched by a Brauer class
 </a>\nby Daniel Chan (UNSW Sydney) as part of ZAG (Zoom Algebraic Geometry
 ) seminar\n\n\nAbstract\nMori's minimal model program is a major organisin
 g principle for studying and classifying varieties $X$. It has been genera
 lised in many directions\, and in this talk\, we examine a ``noncommutativ
 e'' one where $X$ is enriched by a Brauer class $\\beta \\in K(X)$. We foc
 us on some new results where $X$ is a surface whose residue fields are fin
 ite. When the order of $\\beta$ is a prime >5\, we recover most of standar
 d surface theory including existence of terminal resolutions\, Castelnuovo
  contraction and Zariski factorisation. However\, interesting new examples
  of terminal singularities and Castelnuovo contractions appear\, which hav
 e no characteristic zero analogue.\n
LOCATION:https://researchseminars.org/talk/ZAG/210/
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