Author Archives: Jim Stankewicz

The Weil Pairing

Posted on March 26, 2009 by Jim Stankewicz

A nice thing about elliptic curves is the wealth of information which is tied up in the isomorphism class of the group. Over the complex numbers, every elliptic curve is where is a lattice of rank 2 contained in the … Continue reading →

Posted in Abelian Varieties, AG From the Beginning, Curves, Uncategorized | 3 Comments

The Dual Isogeny II

Posted on March 6, 2009 by Jim Stankewicz

Apologies that I haven’t been posting recently. Sage days was this past weekend along with 6 inches of snow in Georgia(read: power outages), the Arizona Winter school in a week and everything else, it’s been very busy.

Posted in Abelian Varieties, AG From the Beginning, Curves, Uncategorized | 1 Comment

The Dual Isogeny

Posted on February 14, 2009 by Jim Stankewicz

Dear Readers, Today I want to talk about morphisms between curves and the special properties they have. This is sort of a broad-based topic, given that the study of morphisms and their properties is essentially the whole of algebraic geometry. … Continue reading →

Posted in Uncategorized | 5 Comments

Elliptic Curves and Jacobians

Posted on February 3, 2009 by Jim Stankewicz

Dear Readers, Today we begin by talking about elliptic curves. We define an elliptic curve to be an abstract nonsingular genus one curve over a field with a given rational point. I’m told the theory of genus one curves without … Continue reading →

Posted in Abelian Varieties, Curves | 3 Comments

An Author in Arithmetic Geometry

Posted on January 28, 2009 by Jim Stankewicz

Hello Readers, My name is Jim and I’m a grad student in arithmetic geometry and algebraic number theory at the University of Georgia. I’m studying for my oral exams and I’ve been invited to use this space, as Charles has, … Continue reading →

Posted in Uncategorized | 2 Comments