中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人： 叶谨赫 博士（Institut de Mathématiques de Jussieu-Paris Rive Gauche）
题 目：Curve-excluding fields
时 间：2022.04.13（星期三），16:00-17:00
地 点：腾讯会议：168-360-966
摘 要：Consider the class of fields with Char(K)=0 and x^4+y^4=1 has only 4 solutions in K, we show that this class has a model companion, which we denote by curve-excluding fields. Curve-excluding fields provide (counter)examples to various questions. Model theoretically, they are model complete, and TP_2. Field theoretically, they are not large and unbounded. Furthermore, they resemble Hilbertian PAC fields to a great extent. We will discuss other aspects such as relative quantifier eliminations, decidability and inverse Galois problems of such fields. This is joint work with Will Johnson and Erik Walsberg.