The period-index problem for elliptic curves and the essential dimension of Picard stacks

Abstract

In this paper, we will consider the period index problems of elliptic curves and introduce a value called generic index which is closed related to the essential dimension of Picard stacks. In particular, we will use examples to see that usually the period and generic index are different. Our construction is different with Cassel's example.

Add the reference for the genericity theorem of $G_m$ gerbes