 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.