Classification of Vector Bundles on Elliptic curves

I'm supposed to give a talk on this subject for one of my courses, so I consider this post as a "pre-exposition." I learned from and heavily used the great exposition "Vector bundles on curves" by Montserrat Teixidor I Bigas in this post. I wrote up the pre-requisites here. In 1957, Atiyah in this famous paper "Vector bundles over … Continue reading Classification of Vector Bundles on Elliptic curves →

Some Homological Algebra Computations

In this post, I'm going to write down the detailed proofs of some of the exercises in Rotman's Homological Algebra. They were asked in ML and then answered by me. 1. Let $latex A$ be a torsion abelian group. Then $latex \text{Ext}^1_\mathbb{Z}(A, \mathbb{Z}) \cong \text{Hom}_\mathbb{Z}(A,S^1)$, where $latex S^1$ is the unit circle. One point is … Continue reading Some Homological Algebra Computations →