19 citations · 28 across the 7 of their papers we have counts for
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math.NT2008★ 4 cited
Period, index and potential sha
Pete L. Clark, Shahed Sharif
In this paper we advance the theory of O'Neil's period-index obstruction map and derive consequences for the arithmetic of genus one curves over global fields. Our first result imp…
math.NT2008★ 1 cited
Period and index of genus one curves over number fields
Shahed Sharif
The period of a curve is the smallest positive degree of Galois-invariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of…