Linden, Georg: Equivariant Vector Bundles on the Drinfeld Upper Half Space over a Local Field of Positive Characteristic. Wuppertal, 2023
Inhalt
- Introduction
- 1. Locally Analytic Representation Theory
- 1.1. Non-Archimedean Manifolds
- 1.2. Locally Analytic Functions
- 1.3. Locally Analytic Representations
- 1.4. Modules over Locally Analytic Distribution Algebras
- 1.5. Locally Analytic Induction
- 1.6. The Hyperalgebra
- 1.7. Non-Archimedean Manifolds Arising from Rigid Analytic Spaces
- 2. H0(X,E)'b and Local Cohomology Groups as Locally Analytic Representations
- 2.1. Topologies on the Coherent and Local Cohomology of Rigid Analytic Spaces
- 2.2. Coherent (Local) Cohomology of Equivariant Vector Bundles
- 2.3. Coherent Cohomology of the Drinfeld Upper Half Space
- 2.4. Strictness of certain Čech Complexes for the Complement of Schubert Varieties
- 2.5. Local Cohomology with respect to Tubes around Schubert Varieties
- 2.6. Local Cohomology Groups with respect to Schubert Varieties as Locally Analytic Representations
- 3. The GLd+1(K)-Representation H0(X,E)
- 3.1. Orlik's Fundamental Complex and the Associated Spectral Sequence
- 3.2. The Subquotients of H0(X,E)'b as Locally Analytic GLd+1(OK)-Representations
- 3.3. The Subquotients of H0(X,E)'b as Locally Analytic GLd+1(K)-Representations
- 3.4. The Functors FPG of Orlik–Strauch
- Appendix A. Non-Archimedean Functional Analysis
- Appendix B. Continuous and Locally Analytic Characters
- References