Arithmetic of diagonal quartic surfaces, II
Arithmetic of diagonal quartic surfaces, II
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对角四次曲面的算术，II
DOI：
10.1112/s0024611500012302
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发表时间：
2000
影响因子：
1.8
通讯作者：
P. Swinnerton
中科院分区：
文献类型：
--
作者：
P. Swinnerton
作者研究形式为a0X04+a1X14+a2X24+a3X34=0的方程的有理数解，其中a0a1a2a3是一个正方形，建立在Colliot-Thène、Skorobogatov和他所发展的思想之上；见发明。数学课。134(1998)579-650。他得到了可解性的充分条件，这似乎与没有布劳尔-马宁障碍有关。这代表了几乎满足Hasse原理的第一大K3曲面族，在这个意义上，确保局部处处可解的辅助条件几乎总是被满足的。1991年数学科目分类：10B10。
The author investigates the solubility in rationals of equations of the form a0X04+a1X14+a2X24+a3X34=0 where a0a1a2a3 is a square, building on the ideas which Colliot‐Thène, Skorobogatov and he have developed; see Invent. Math. 134 (1998) 579–650. He obtains sufficient conditions for solubility, which appear to be related to the absence of a Brauer–Manin obstruction. This represents the first large family of K3 surfaces which almost satisfy the Hasse principle, in the sense that the auxiliary condition which ensures that local solubility everywhere implies global solubility is nearly always satisfied. 1991 Mathematics Subject Classification: 10B10.