Math @ Duke

Publications [#167242] of Shahed Sharif
Papers Published
 S. Sharif, Curves of prescribed period and index over local fields, edited by David Goss,
Journal of Number Theory, vol. 314 no. 1
(Spring, 2007),
pp. 157167, Elsevier, ISSN 0022314X
(last updated on 2009/12/17)
Abstract: The index of a curve is the smallest positive degree of divisors which are rational over a fixed base field. The period is the smallest positive degree of divisor classes rational over the base field. Lichtenbaum proved certain divisibility conditions relating the period, index, and genus of a curve over a local field. We prove that his conditions are sharp by finding a curve of every admissible period, index, and genus. Our proof constructs degree two covers of elliptic curves with split multiplicative reduction.


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