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math.NT2014
Bad reduction of genus curves with complex multiplication
Irene Bouw, Jenny Cooley, Kristin Lauter +4
Let be a smooth, absolutely irreducible genus- curve over a number field . Suppose that the Jacobian of has complex multiplication by a sextic CM-field . Suppose f…
math.NT2013
Cubic surfaces with one rational line over finite fields
Jenny Cooley
Let Fq be a finite field with q=8 or q at least 16. Let S be a smooth cubic surface defined over Fq containing at least one rational line. We use a pigeonhole principle to prove th…
math.NT2012
Generators for Cubic Surfaces with two Skew Lines over Finite Fields
Jenny Cooley
Let S be a smooth cubic surface defined over a field K. As observed by Segre and Manin, there is a secant and tangent process on S that generates new K-rational points from old. It…