Diagonal quartic surfaces with a Brauer-Manin obstruction

被引：1
|
作者：
Santens, Tim [1 ]
机构：
[1] Katholieke Univ Leuven, Dept wiskunde, Celestijnenlaan 200B, B-3001 Leuven, Belgium
来源：
COMPOSITIO MATHEMATICA | 2023年 / 159卷 / 04期
关键词：
quartic surfaces; rational points; Brauer-Manin obstruction; Artin L-series; HASSE PRINCIPLE; POINTS; NUMBER;
D O I：
10.1112/S0010437X22007916
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we investigate the quantity of diagonal quartic surfaces a(0)X(0)(4) + a(1)X(1)(4) + a(2)X(2)(4) + a(3)X(3)(4) = 0 which have a Brauer-Manin obstruction to the Hasse principle. We are able to find an asymptotic formula for the quantity of such surfaces ordered by height. The proof uses a generalization of a method of Heath-Brown on sums over linked variables. We also show that there exists no uniform formula for a generic generator in this family.
引用
收藏
页码：659 / 710
页数：53
相关论文
共 50 条
  • [1] Odd order Brauer-Manin obstruction on diagonal quartic surfaces
    Ieronymou, Evis
    Skorobogatov, Alexei N.
    ADVANCES IN MATHEMATICS, 2015, 270 : 181 - 205
  • [2] The Brauer-Manin obstruction on a general diagonal quartic surface
    Bright, Martin
    ACTA ARITHMETICA, 2011, 147 (03) : 291 - 302
  • [3] Odd order Brauer-Manin obstruction on diagonal quartic surfaces (vol 270, pg 181, 2015)
    Ieronymou, Evis
    Skorobogatov, Alexei N.
    ADVANCES IN MATHEMATICS, 2017, 307 : 1372 - 1377
  • [4] The Brauer-Manin obstruction for certain quartic curves with negative discriminant
    Nguyen Ngoc Dong Quan
    COMMUNICATIONS IN ALGEBRA, 2017, 45 (02) : 455 - 468
  • [5] Degree and the Brauer-Manin obstruction
    Creutz, Brendan
    Viray, Bianca
    Skorobogatov, Alexei N.
    ALGEBRA & NUMBER THEORY, 2018, 12 (10) : 2445 - 2470
  • [6] Noninvariance of weak approximation with Brauer-Manin obstruction for surfaces
    Wu, H. A. N.
    ACTA ARITHMETICA, 2022, : 21 - 32
  • [7] Heuristics for the Brauer-Manin obstruction for curves
    Poonen, Bjorn
    EXPERIMENTAL MATHEMATICS, 2006, 15 (04) : 415 - 420
  • [8] Insufficiency of the Brauer-Manin Obstruction for Rational Points on Enriques Surfaces
    Balestrieri, Francesca
    Berg, Jennifer
    Manes, Michelle
    Park, Jennifer
    Viray, Bianca
    DIRECTIONS IN NUMBER THEORY, 2016, 3 : 1 - 31
  • [9] SINGULAR CURVES AND THE ETALE BRAUER-MANIN OBSTRUCTION FOR SURFACES
    Harpaz, Yonatan
    Skorobogatov, Alexei N.
    ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2014, 47 (04): : 765 - 778
  • [10] Pathologies of the Brauer-Manin obstruction
    Colliot-Thelene, Jean-Louis
    Pal, Ambrus
    Skorobogatov, Alexei N.
    MATHEMATISCHE ZEITSCHRIFT, 2016, 282 (3-4) : 799 - 817
12345