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Linden, Georg: Equivariant Vector Bundles on the Drinfeld Upper Half Space over a Local Field of Positive Characteristic. Wuppertal, 2023
Content
Introduction
Acknowledgements
Notation and Conventions
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
B.1. Continuous Characters
B.2. Locally Analytic Characters
References