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Smooth projective stacks : ample bundles and D-affinity

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El Haloui, Karim (2018) Smooth projective stacks : ample bundles and D-affinity. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b3226884~S15

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Abstract

This thesis is on the study of sheaves of O-modules and D-modules on projective stacks. In chapter 1, a historical perspective is given on the main fidings that have shaped and influenced the study carried out and exposed in this thesis. In chapter 2, the principal definitions and results used in the forthcoming sections are recalled. An appendix is added at the end of this chapter exposing self-containedly why quotient singularities and orbifolds are two equivalent notions. In chapter 3, the property of ampleness of vector bundles on projective stacks is generalised and studied. Basic properties are given; in particular it is proved that weighted projective stacks have ample tangent vector bundle. In chapter 4, D-modules on projective stacks are studied. General conditions on the weights and the shift guaranteeing a weighted projective stack to be D-affine are given. Thus, proving a version of the Beilinson-Bernstein Localisation Theorem. In particular, a weighted projective stack is D-affine if and only if the greatest common divisor of its weights is one. A theorem of Kashiwara is extended to smooth projective stacks, it is shown that the category of D-modules on a smooth closed projective substack [X] is equivalent to the category of D-modules on the ambient smooth projective stack [Y ] supported on [X].

Item Type: Thesis (PhD)
Subjects: Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH): Geometry, Algebraic, Algebraic stacks, Geometry, Projective, Sheaf theory, Vector bundles, Geometry, Affine
Official Date: May 2018
Dates:
DateEvent
May 2018Submitted
Institution: University of Warwick
Theses Department: Mathematics Institute
Thesis Type: PhD
Publication Status: Unpublished
Supervisor(s)/Advisor: Rumynin, Dmitriy, 1971-
Format of File: pdf
Extent: vii, 108 leaves
Language: eng

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