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D-modules on rigid analytic spaces

Abstract:
We introduce a sheaf of infinite order differential operators D on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent bundle. We show that the sections of this sheaf over sufficiently small affinoid varieties are Fréchet-Stein algebras, and use this to define co-admissible sheaves of D-modules. We prove analogues of Cartan’s Theorems A and B for co-admissible D-modules.
Publication status:
Published
Peer review status:
Peer reviewed

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Files:
Publisher copy:
10.1515/crelle-2016-0016

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
De Gruyter Publisher's website
Journal:
Journal für die reine und angewandte Mathematik Journal website
Publication date:
2016-07-12
DOI:
EISSN:
0075-4102
ISSN:
1435-5345
Pubs id:
pubs:599370
UUID:
uuid:a0342caf-2b1d-4f7d-9a4c-73a7774b1f26
Local pid:
pubs:599370
Source identifiers:
599370
Deposit date:
2016-02-06

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