, Volume 115, Issue 4, pp 437-466
Date: 05 Nov 2004

The Hasse principle and the Brauer-Manin obstruction for curves

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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.

Mathematics Subject Classification (2000): Primary 11G30; Secondary 11G10, 14H40
The author was supported by EPSRC grant GR/R82975/01.