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SUMMARY:Jinhe Ye (University of Oxford)
DTSTART:20241010T180000Z
DTEND:20241010T190000Z
DTSTAMP:20260513T204417Z
UID:OLS/156
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/156/">Hy
 perbolicity and model complete fields</a>\nby Jinhe Ye (University of Oxfo
 rd) as part of Online logic seminar\n\n\nAbstract\nGiven $C$ a (quasi-proj
 ective) curve over $\\mathbb{Q}$ with genus at least 2 and $C(\\mathbb{Q})
 $ is empty\, the class of fields $K$ of characteristic 0 such that $C(K)=\
 \emptyset$ has a model companion CXF. Models of CXF have an interesting co
 mbination of properties and provide examples to answer various questions a
 round model theory of fields\, field arithmetic\, and decidability.\n\nIt 
 turns out the existence of model companion is related to several notions o
 f hyperbolicity in algebraic geometry. In particular\, with the assumption
 s of different notions of hyperbolicity on V\, our results admit generalis
 ation to varieties V of arbitrary dimension. This talk is based on joint w
 ork with Will Johnson and joint work with Michal Szachniewicz.\n
LOCATION:https://researchseminars.org/talk/OLS/156/
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