颤振中的Frobenian乘法函数和有理点

IF 2.5 1区数学 Q1 MATHEMATICS

Journal of the European Mathematical Society Pub Date : 2023-09-15 DOI:10.4171/jems/1374

Daniel Loughran, Lilian Matthiesen

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引用次数: 7

摘要

我们考虑在$\mathbb{Q}$上有一个有理点的一族中计算变种数的问题。对于$\mathbb{P}^1$上的一些族，我们得到了这个计数问题的下界，即使Hasse原理失效。在高维投影空间上，我们也得到了一些多项式方程和某些Brauer群元的专门化的尖锐结果，其中我们回答了Serre问题的一些情况。我们的技术来自算术几何和加性组合学。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Frobenian multiplicative functions and rational points in fibrations

We consider the problem of counting the number of varieties in a family over $\mathbb{Q}$ with a rational point. We obtain lower bounds for this counting problem for some families over $\mathbb{P}^1$, even if the Hasse principle fails. We also obtain sharp results for some multinorm equations and for specialisations of certain Brauer group elements on higher-dimensional projective spaces, where we answer some cases of a question of Serre. Our techniques come from arithmetic geometry and additive combinatorics.

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来源期刊

Journal of the European Mathematical Society 数学-数学

CiteScore

4.50

自引率

0.00%

发文量

103

审稿时长

6-12 weeks

期刊介绍： The Journal of the European Mathematical Society (JEMS) is the official journal of the EMS. The Society, founded in 1990, works at promoting joint scientific efforts between the many different structures that characterize European mathematics. JEMS will publish research articles in all active areas of pure and applied mathematics. These will be selected by a distinguished, international board of editors for their outstanding quality and interest, according to the highest international standards. Occasionally, substantial survey papers on topics of exceptional interest will also be published. Starting in 1999, the Journal was published by Springer-Verlag until the end of 2003. Since 2004 it is published by the EMS Publishing House. The first Editor-in-Chief of the Journal was J. Jost, succeeded by H. Brezis in 2004. The Journal of the European Mathematical Society is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.