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May  2010, 4(2): 101-114. doi: 10.3934/amc.2010.4.101

Local-global aspects of (hyper)elliptic curves over (in)finite fields

Joseph H. Silverman 1,

1. 

Mathematics Department, Box 1917, Brown University, Providence, RI 02912, United States

Received  May 2009 Revised  July 2009 Published  May 2010

We survey the interaction between local and global theory for studying the arithmetic properties of curves, jacobians, and abelian varieties.
Keywords: Elliptic curve, abelian variety., hyperelliptic curve.
Mathematics Subject Classification: Primary: 11G05; Secondary: 11G3.
Citation: Joseph H. Silverman. Local-global aspects of (hyper)elliptic curves over (in)finite fields. Advances in Mathematics of Communications, 2010, 4 (2) : 101-114. doi: 10.3934/amc.2010.4.101
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