Abstract: For a given étale l-adic sheaf F on rigid space X, the Swan conductor, a measure of wild ramification of F along the special fiber of a formal model of X, is the l-adic analog of the radius of convergence of solutions of p-adic differential equations on X. I will show (when X is an annulus) that the function defined by the Swan conductor has properties that mirror those of the radius of convergence function.