Polarisierungen der Jacobi-Varietäten von Mumford-Kurven

Abstract

We describe the construction of the Jacobian of a Mumford curve of genus g as a rigid analytic quotient of an affine g-dimensional torus by a lattice M of full rank g. We define two canonical principal polarizations of M, namely Drinfeld´s and the Theta polarization. Our main result states that these two polarizations actually coincide. This can be viewed as a reformulation of Riemann´s Vanishing Theorem.