We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
$\widehat {\mathcal {D}}$-modules on rigid analytic spaces III: weak holonomicity and operations
We develop a dimension theory for coadmissible 
$\widehat {\mathcal {D}}$-modules on rigid analytic spaces and study those which are of minimal dimension, in analogy to the theory of holonomic 
$\mathcal {D}$-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 
$\underline {H}^{i}_Z(\mathcal {M})$ with support in a closed analytic subset 
$Z$ of 
$X$ are also coadmissible of minimal dimension for any integrable connection 
$\mathcal {M}$ on 
$X$.
