The Mathematical Institute, University of Oxford, Eprints Archive

The Hasse principle and the Brauer-Manin obstruction for curves

Flynn, E. V. (2004) The Hasse principle and the Brauer-Manin obstruction for curves. Manuscripta Mathematica, 115 . pp. 437-466. ISSN 0025-2611

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Hasse Principle, Jacobians, Brauer-Manin Obstruction
Subjects:A - C > Algebraic geometry
H - N > Number theory
Research Groups:Number Theory Group
ID Code:253
Deposited By:E. Victor Flynn
Deposited On:12 Jul 2006
Last Modified:20 Jul 2009 14:19

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