Rational points on fibrations with few non-split fibres

doi:10.1515/crelle-2022-0042

	Rational points on fibrations with few non-split fibres
	Harpaz, Yonatan 1; Wei, Dasheng 2,3; Wittenberg, Olivier 1
刊名	JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
	2022-08-12
页码	45
ISSN号	0075-4102
DOI	10.1515/crelle-2022-0042
英文摘要	We revisit the abstract framework underlying the fibration method for producing rational points on the total space of fibrations over the projective line. By fine-tuning its dependence on external arithmetic conjectures, we render the method unconditional when the degree of the non-split locus is <= 2 , as well as in various instances where it is 3. We are also able to obtain improved results in the regime that is conditionally accessible under Schinzel's hypothesis, by incorporating into it, for the first time, a technique due to Harari for controlling the Brauer-Manin obstruction in families.
资助项目	National Key R&D Program of China ; National Natural Science Foundation of China[11622111] ; National Natural Science Foundation of China[11631009]
WOS研究方向	Mathematics
语种	英语
出版者	WALTER DE GRUYTER GMBH
WOS记录号	WOS:000838819200001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61090]
专题	中国科学院数学与系统科学研究院
通讯作者	Wittenberg, Olivier
作者单位	1.Univ Sorbonne Paris Nord, Inst Galilee, 99 Ave Jean Baptiste Clement, F-93430 Villetaneuse, France 2.Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 3.Univ CAS, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Harpaz, Yonatan,Wei, Dasheng,Wittenberg, Olivier. Rational points on fibrations with few non-split fibres[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK,2022:45.
APA	Harpaz, Yonatan,Wei, Dasheng,&Wittenberg, Olivier.(2022).Rational points on fibrations with few non-split fibres.JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK,45.
MLA	Harpaz, Yonatan,et al."Rational points on fibrations with few non-split fibres".JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK (2022):45.