Department of Mathematics

Algebra

  •  
  •  From Picard groups of hyperelliptic curves to class groups of quadratic fields
  •  05/22/2018
  •  1:00 PM - 2:00 PM
  •  C304 Wells Hall

Let C be a hyperelliptic curve defined over Q, whose Weierstrass points are defined over extensions of Q of degree at most three, and at least one of them is rational. Generalizing a result of R. Soleng (in the case of elliptic curves), we prove that any line bundle of degree 0 on C which is not torsion can be specialized into ideal classes of imaginary quadratic fields whose order can be made arbitrarily large. This gives a positive answer, for such curves, to a question by Agboola and Pappas.

 

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Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
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