Publications [#167242] of Shahed Sharif

Papers Published

1. 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. 157-167, Elsevier, ISSN 0022-314X
   (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.