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

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Optimization of the arithmetic of the ideal class group for genus 4 hyperelliptic curves over projective coordinates

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

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

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

Received May 2009 Revised July 2009 Published May 2010

Abstract
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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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