### The skeleton of the Jacobian and the Jacobian of the skeleton

- Series
- Algebra Seminar
- Time
- Monday, December 2, 2013 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Joseph Rabinoff – Georgia Tech – rabinoff@math.gatech.edu

Let X be an algebraic curve over a non-archimedean field K. If the
genus of X is at least 2 then X has a minimal skeleton S(X), which is
a metric graph of genus <= g. A metric graph has a Jacobian J(S(X)),
which is a principally polarized real torus whose dimension is the
genus of S(X). The Jacobian J(X) also has a skeleton S(J(X)), defined
in terms of the non-Archimedean uniformization theory of J(X), and
which is again a principally polarized real torus with the same
dimension as J(S(X)). I'll explain why S(J(X)) and J(S(X)) are
canonically isomorphic, and I'll indicate what this isomorphism has to
do with several classical theorems of Raynaud in arithmetic geometry.