### About this blog

Rigorous trivialities is a web log about mathematics, but especially geometry, broadly construed. Contributors will be Charles Siegel, Jim Stankewicz and occasionally Matt Deland. Charles specializes in algebraic geometry, topology and mathematical physics. Jim specializes in arithmetic algebraic geometry. Matt has transitioned from algebraic geometry to work in industry.

Header is taken from the larger work by fdecomite under the creative commons license.

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# Author Archives: Jim Stankewicz

## The Weil Pairing

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

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

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

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

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