首师大数论组讨论班（2015-11-25）
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SHUN TANG
Nov 15, 2015, 11:57:41 PM11/15/15
to Celtic Zhang, cnuarith, Derong Qiu, dshwei, gnge, Hui Gao, jiangxue fang, Jinpeng An, kinglaihonkon, kzli, Peng Sun, Ruochuan Liu, Weizhe Zheng, wuke, xufei, yichaot, Yonghui Wang, Zhibin Liang, 孙晟昊, 李克正, 许晨阳, bbyingjin, 张翀, 梁庭嘉, Yongquan Hu, matht...@outlook.com, sy...@math.tsinghua.edu.cn
诸位好，本学期首都师范大学第五次数论与代数几何讨论班将于下周举行：
时间：2015年11月25日 周三 上午 10：30--11：30
地点：首都师范大学北二区教学楼513教室（此校区位于西三环紫竹桥南首师大北一区的街对面，走一个过街天桥即到）
报告人：Prof. J.-L. Colliot-Thélène
（CNRS and Université Paris-Sud-Paris-Saclay, France）
题目：The set of non-n-th powers is a diophantine set
摘要：A subset of a number field k is called diophantine if it is the image of the set of rational points of some affine variety under a morphism to the affine line, i.e. if is the set of values of a function on the variety. For n = 2 the statement in the title is a theorem of B. Poonen (2009). He uses a one-parameter family of varieties together with a theorem of Coray, Sansuc and the speaker (1980), on the Brauer–Manin obstruction for rational points on these varieties. For n = p, p any prime number, A. Várilly-Alvarado and B. Viray (2012) considered an analogous family of varieties. Replacing this family by its (2p+1)th symmetric power, we prove the statement in the title using a theorem on the Brauer–Manin obstruction for rational points on such symmetric powers. The latter theorem is based on work of one of the authors with Swinnerton-Dyer (1994) and with Skorobogatov and Swinnerton-Dyer (1998), work generalising results of Salberger (1988).
请将此信息转发给其他感兴趣的老师和学生，期待与大家相会！
祝好！
唐舜
--
时间：2015年11月25日 周三 上午 10：30--11：30
地点：首都师范大学北二区教学楼513教室（此校区位于西三环紫竹桥南首师大北一区的街对面，走一个过街天桥即到）
报告人：Prof. J.-L. Colliot-Thélène
（CNRS and Université Paris-Sud-Paris-Saclay, France）
题目：The set of non-n-th powers is a diophantine set
摘要：A subset of a number field k is called diophantine if it is the image of the set of rational points of some affine variety under a morphism to the affine line, i.e. if is the set of values of a function on the variety. For n = 2 the statement in the title is a theorem of B. Poonen (2009). He uses a one-parameter family of varieties together with a theorem of Coray, Sansuc and the speaker (1980), on the Brauer–Manin obstruction for rational points on these varieties. For n = p, p any prime number, A. Várilly-Alvarado and B. Viray (2012) considered an analogous family of varieties. Replacing this family by its (2p+1)th symmetric power, we prove the statement in the title using a theorem on the Brauer–Manin obstruction for rational points on such symmetric powers. The latter theorem is based on work of one of the authors with Swinnerton-Dyer (1994) and with Skorobogatov and Swinnerton-Dyer (1998), work generalising results of Salberger (1988).
请将此信息转发给其他感兴趣的老师和学生，期待与大家相会！
祝好！
唐舜
--
Shun TANG
School of Mathematical Sciences
Capital Normal University
No. 105, West 3rd Ring North Road
100048, Beijing
P. R. China
School of Mathematical Sciences
Capital Normal University
No. 105, West 3rd Ring North Road
100048, Beijing
P. R. China
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