D-modules on rigid analytic spaces III: weak holonomicity and operations. (28th December 2021) - Ardakov, Konstantin; Bode, Andreas; Wadsley, Simon
Abstract: We develop a dimension theory for coadmissible D -modules on rigid analytic spaces and study those which are of minimal dimension, in analogy to the theory of holonomic D -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 H^i_Z(M) with support in a closed analytic subset Z of X are also coadmissible of minimal dimension for any integrable connection M on X .