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Mathematics

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Mathematics

 
 

Recent Submissions

  • Period, index, and potential Sha 
    Clark, Pete; Sharif, Shahed (Algebra and Number Theory, 2010)
    We present three results on the period-index problem for genus-one curves over global fields. Our first result implies that for every pair of positive integers (P, I) such that I is divisible by P and divides P 2 , ...
  • Period and index of genus one curves over number fields 
    Sharif, Shahed (Mathematische Annalen, 2012-11)
    The period of a curve is the smallest positive degree of Galoisinvariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of genus one curves with prescribed period and ...
  • A descent map for curves with totally degenerate semi-stable reduction 
    Sharif, Shahed (Journal de Théorie des Nombres de Bordeaux, 2013)
    Let $K$ be a local field of residue characteristic $p$. Let $C$ be a curve over $K$ whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to-$p$ ...