Monday, December 2, 2013 - 3:00pm
1 hour (actually 50 minutes)
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.