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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.