D-modules on rigid analytic spaces III: weak holonomicity and operations
We develop a dimension theory for coadmissible D-cap-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...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Cambridge University Press
2021
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| Summary: | We develop a dimension theory for coadmissible D-cap-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,
infinte-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 $H^i_Z(\mathcal{M})$
with support in a closed analytic subset $Z$ of $X$ are also coadmissible of
minimal dimension for any integrable connection $\mathcal{M}$ on $X$. |
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