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Curve-excluding fields

发布人:发布时间: 2022-12-13

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题目:Curve-excluding fields


报告人:叶谨赫 Jinhe Ye(University of Oxford)


时间:2022年12月22日(周四)上午10:00


地点:鼓楼校区西大楼108报告厅


线上直播:腾讯会议    ID: 203-455-393    密码:221222


摘要:Consider the class of fields with Char$(K)=0$ such that $x^4+y^4=1$ has only 4 solutions in $K$. Following the philosophy of Artin and Lang of "digging holes in the algebraic closure", we show that the “maximal objects” in the class, curve-excluding fields, admit nice axiomtization. Curve-excluding fields provide counterexamples to various open questions in field arithmetic and model theory. To highlight a few of their properties, they are model complete and algebraically bounded model-theoretically,. Field-theoretically, they can be non-large when we vary the curve of choice.  Moreover, there exist decidable curve-excluding fields, which provides a decidable non-large unbounded field. This is based on joint work with Will Johnson and Erik Walsberg.