Introduction to moduli, l-adic representations and the Regular Version of the Inverse Galois Problem

Abstract

There are two famous Abel Theorems. The more well-known, describes the "abelian (analytic) functions" on a one dimensional compact complex torus. The other bundles those complex tori, with their prime degree isogenies. Riemann's generalization of the first features his famous Θ functions. His deepest work aimed to generalize Abel's second theorem, though he died too young to fulfill that vision.