Rational points on fibrations with few non-split fibres

doi:10.1515/crelle-2022-0042

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	Rational points on fibrations with few non-split fibres
	Harpaz, Yonatan 1; Wei, Dasheng 2,3; Wittenberg, Olivier 1
	2022-08-12
发表期刊	JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
ISSN	0075-4102
页码	45
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.
DOI	10.1515/crelle-2022-0042
收录类别	SCI
语种	英语
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
WOS类目	Mathematics
WOS记录号	WOS:000838819200001
出版者	WALTER DE GRUYTER GMBH
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61091
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.