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Towards affinoid Duflo’s theorem I: twisted differential operators

Part of: Analytic spaces Algebraic groups

Published online by Cambridge University Press:  13 April 2021

IOAN STANCIU
IOAN STANCIU*
Affiliation:
Mathematical Institute, Andrew Wiles building, Radcliffe Observatory Quarter, Woodstock Road, University of Oxford, Oxford, OX2 6GG e-mail: ioan.stanciu@maths.ox.ac.uk
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Abstract

For a commutative ring R, we define the notions of deformed Picard algebroids and deformed twisted differential operators on a smooth, separated, locally of finite type R-scheme and prove these are in a natural bijection. We then define the pullback of a sheaf of twisted differential operators that reduces to the classical definition when R = ℂ. Finally, for modules over twisted differential operators, we prove a theorem for the descent under a locally trivial torsor.

MSC classification

Primary: 32C38: Sheaves of differential operators and their modules, $D$-modules
Secondary: 14L30: Group actions on varieties or schemes (quotients)
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 172 , Issue 3 , May 2022 , pp. 531 - 561
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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