manuscripta mathematica

, Volume 115, Issue 4, pp 437–466

The Hasse principle and the Brauer-Manin obstruction for curves

Authors

    • Department Mathematical SciencesUniversity of Liverpool
Article

DOI: 10.1007/s00229-004-0502-9

Cite this article as:
Flynn, E. manuscripta math. (2004) 115: 437. doi:10.1007/s00229-004-0502-9

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.

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© Springer-Verlag Berlin Heidelberg 2004