Projective generation for equivariant D-modules

Bellamy, G. , Gunningham, S. and Raskin, S. (2022) Projective generation for equivariant D-modules. Transformation Groups, 27(3), pp. 737-749. (doi: 10.1007/s00031-021-09660-1)

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We investigate compact projective generators in the category of equivariant D-modules on a smooth affine variety. For a reductive group G acting on a smooth affine variety X, there is a natural countable set of compact projective generators indexed by finite dimensional representations of G. We show that only finitely many of these objects are required to generate; thus the category has a single compact projective generator. The proof in the general case goes via an analogous statement about compact generators in the equivariant derived category, which holds in much greater generality and may be of independent interest.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bellamy, Professor Gwyn
Authors: Bellamy, G., Gunningham, S., and Raskin, S.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Transformation Groups
ISSN (Online):1531-586X
Published Online:01 June 2021
Copyright Holders:Copyright © 2021 The Authors
First Published:First published in Transformation Groups 27(3): 737-749
Publisher Policy:Reproduced under a Creative Commons licence
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