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Journal fĂĽr die reine und angewandte Mathematik

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Volume 2019, Issue 747


⌢𝒟-modules on rigid analytic spaces I

Konstantin ArdakovORCID iD: https://orcid.org/0000-0002-5011-022X / Simon J. Wadsley
Published Online: 2016-07-12 | DOI: https://doi.org/10.1515/crelle-2016-0016


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.


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About the article

Received: 2015-06-28

Revised: 2016-02-03

Published Online: 2016-07-12

Published in Print: 2019-02-01

Funding Source: Engineering and Physical Sciences Research Council

Award identifier / Grant number: EP/L005190/1

The first author was supported by EPSRC grant EP/L005190/1.

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2019, Issue 747, Pages 221–275, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2016-0016.

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