两二次曲线交点的有效哈塞原理

Q1 Mathematics

Lms Journal of Computation and Mathematics Pub Date : 2016-02-16 DOI:10.1112/S146115701600022X

Tony Quertier

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引用次数: 3

摘要

我们考虑至少有13个变量的有理数上的两个齐次二次方程的光滑系统。在这种情况下，由于莫德尔在1959年的工作，Hasse原理被认为是成立的。唯一的地方障碍是在公路上。本文给出了一种确定非零有理解是否存在的显式算法，如果存在则计算非零有理解。

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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Effective Hasse principle for the intersection of two quadrics

We consider a smooth system of two homogeneous quadratic equations over the rationals in at least 13 variables. In this case, the Hasse principle is known to hold, thanks to the work of Mordell in 1959. The only local obstruction is over the reals. In this paper, we give an explicit algorithm to decide whether a nonzero rational solution exists, and if so, to compute one.

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来源期刊

Lms Journal of Computation and Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.