Equivariant vector bundles and rigid cohomology on Drinfeld's upper half space over a finite field / vorgelegt von Mark Kuschkowitz aus Halle/Saale. Wuppertal, März 2016
Content
- Introduction
- Preliminaries
- General Notation
- Representations
- Induced Representations
- Composition Series and Semisimplifications
- (Generalized) Steinberg Representations
- The Simple (Algebraic) Representations of Gk and G, and Weyl Modules
- Drinfeld's Upper Half Space over a Finite Field
- Sheaves and Cohomology
- Cohomology of Equivariant Vector Bundles on Drinfeld's Upper Half Space over a Finite Field
- Orlik's Complex for the Cohomology of Equivariant Vector Bundles
- Construction of the Complex
- An Equivariant Filtration on the Cohomology of Drinfeld's Upper Half Space
- Local Cohomology I: First Descriptions
- Bundles arising from Representations of a Levi Subgroup
- Using the Canonical Projection onto a Projective Subvariety
- Local Cohomology II: Failure of ``Classical'' Lie Algebraic Methods
- Generalized Fractions
- The Action of the Universal Enveloping Algebra
- The Action of the Distribution Algebra
- Enriched Crystalline Enveloping Algebras: Adding more Divided Powers to the Distribution Algebra
- Local Cohomology III: Description via Enriched Crystalline Enveloping Algebra
- Employing the Enriched Crystalline Enveloping Algebra
- Functorial Reinterpretation: U+-Algebraic Induction and Extension of Duality
- Examples
- Rigid Cohomology of Drinfeld's Upper Half Space over a Finite Field
- Construction of Rigid Cohomology and some Properties
- Berthelot's Definition of Rigid Cohomology (with and without Supports)
- Some Properties of Rigid Cohomology
- Rigid Cohomology computed as Hypercohomology
- Adaption of Orlik's Complex
- Construction of a Spectral Sequence
- Evaluation of the Spectral Sequence
- Computation of the Rigid Cohomology Modules
- Rigid Cohomology computed from the Associated De Rham Complex
- Bibliography