奇异K3曲面上的先验Brauer-Manin障碍。

IF 0.6 Q3 MATHEMATICS

Research in Number Theory Pub Date : 2025-01-01 Epub Date: 2024-12-18 DOI:10.1007/s40993-024-00580-z

Mohamed Alaa Tawfik, Rachel Newton

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引用次数: 0

摘要

设E和E ‘是Q上的椭圆曲线，它们被虚二次域K的整数环复乘，设Y = Kum （E × E ’）是E × E '商在- 1作用下的最小解形化。我们研究了这类曲面Y的Brauer群，并利用它们给出了弱逼近的超越Brauer- manin障碍的新例子。

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Transcendental Brauer-Manin obstructions on singular K3 surfaces.

Let E and $E^{'}$ be elliptic curves over $Q$ with complex multiplication by the ring of integers of an imaginary quadratic field K and let $Y = Kum (E \times E^{'})$ be the minimal desingularisation of the quotient of $E \times E^{'}$ by the action of $- 1$ . We study the Brauer groups of such surfaces Y and use them to furnish new examples of transcendental Brauer-Manin obstructions to weak approximation.

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来源期刊

Research in Number Theory MATHEMATICS-

CiteScore

0.80

自引率

12.50%

发文量

期刊介绍： Research in Number Theory is an international, peer-reviewed Hybrid Journal covering the scope of the mathematical disciplines of Number Theory and Arithmetic Geometry. The Mission of the Journal is to publish high-quality original articles that make a significant contribution to these research areas. It will also publish shorter research communications (Letters) covering nascent research in some of the burgeoning areas of number theory research. This journal publishes the highest quality papers in all of the traditional areas of number theory research, and it actively seeks to publish seminal papers in the most emerging and interdisciplinary areas here as well. Research in Number Theory also publishes comprehensive reviews.