The Hasse principle and the Brauer-Manin obstruction for curves

被引：26
|
作者：
Flynn, EV [1 ]
机构：
[1] Univ Liverpool, Dept Math Sci, Liverpool L69 3BX, Merseyside, England
来源：
MANUSCRIPTA MATHEMATICA | 2004年 / 115卷 / 04期
关键词：
D O I：
10.1007/s00229-004-0502-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We discuss a range of ways, extending existing methods, to demonstrate violations of the Hasse principle on curves. Of particular interest are curves which contain a rational divisor class of degree 1, even though they contain no rational point. For such curves we construct new types of examples of violations of the Hasse principle which are due to the Brauer-Manin obstruction, subject to the conjecture that the Tate-Shafarevich group of the Jacobian is finite.
引用
收藏
页码：437 / 466
页数：30
相关论文
共 50 条
  • [1] The Hasse principle and the Brauer-Manin obstruction for curves
    E.V. Flynn
    manuscripta mathematica, 2004, 115 : 437 - 466
  • [2] Non-invariance of the Hasse principle with Brauer-Manin obstruction
    Wu, Han
    MANUSCRIPTA MATHEMATICA, 2023, 171 (3-4) : 457 - 471
  • [3] Heuristics for the Brauer-Manin obstruction for curves
    Poonen, Bjorn
    EXPERIMENTAL MATHEMATICS, 2006, 15 (04) : 415 - 420
  • [4] The Brauer-Manin obstruction for integral points on curves
    Harari, David
    Voloch, Jose Felipe
    MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2010, 149 : 413 - 421
  • [5] The d-primary Brauer-Manin obstruction for curves
    Creutz, Brendan
    Viray, Bianca
    Voloch, Jose Felipe
    RESEARCH IN NUMBER THEORY, 2018, 4
  • [6] Transcendental Brauer-Manin obstruction on a pencil of elliptic curves
    Wittenberg, O
    ARITHMETIC OF HIGHER-DIMENSIONAL ALGEBRAIC VARIETIES, 2004, 226 : 259 - 267
  • [7] 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
  • [8] On the Brauer-Manin obstruction for zero-cycles on curves
    Eriksson, Dennis
    Scharaschkin, Victor
    ACTA ARITHMETICA, 2008, 135 (02) : 99 - 110
  • [9] Degree and the Brauer-Manin obstruction
    Creutz, Brendan
    Viray, Bianca
    Skorobogatov, Alexei N.
    ALGEBRA & NUMBER THEORY, 2018, 12 (10) : 2445 - 2470
  • [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