A Lefschetz hyperplane theorem for non-Archimedean Jacobians

We establish a Lefschetz hyperplane theorem for the Berkovich analytifications of Jacobians curves over an algebraically closed non-Archimedean field. Let J be Jacobian curve X, and let $$W_{d} \subset J$$ locus effective divisor classes degree d. show that pair $$(J^{an},W_d^{an})$$ is d-connected, thus in particular inclusion analytification theta $$\Theta ^{an}$$ into $$J^{an}$$ satisfies $${\mathbb {Z}}$$ -cohomology groups homotopy groups. A key ingredient our proof generalization, arbitrary characteristics allowing singularities on base, result Brown Foster type analytic projective bundles.