查看文章

We develop a dimension theory for coadmissible -modules on rigid analytic spaces and study those which are of minimal dimension, in analogy to the theory of holonomic -modules in the algebraic setting. We discuss a number of pathologies contained in this subcategory (modules of infinite length, infinite-dimensional fibres). We prove stability results for closed immersions and the duality functor, and show that all higher direct images of integrable connections restricted to a Zariski open subspace are coadmissible of minimal dimension. It follows that the local cohomology sheaves with support in a closed analytic subset of are also coadmissible of minimal dimension for any integrable connection on .