Divisibility of line sheaves on totally degenerate curves
Time and place
1 PM on Thursday, December 9th, 2010; NAC 6-113
Shahed Sharif (Cooper Union)
Abstract
Let $K$ be either a $p$-adic field or $\mathbb{F}((t))$ for some finite field $\mathbb{F}$. Let $C$ be a curve over $K$ which has totally degenerate reduction. We show how to determine if a Galois-equivariant line sheaf on $C$ is divisible by a given integer $r$ by computations on the special fiber of $C$. Applications include determination of the rationality of theta characteristics and computation of torsion on the Jacobian of $C$. This is a work in progress.
