Automorphic vector bundles on connected Shimura varieties

Abstract

Introduction 0. Review of terminology concerning Shimura varieties 1. The Taniyama group, the period torsor, and conjugates of Shimura varieties 2. The compact dual symmetric Hermitian space and its conjugates 3. The principal bundle Y~ X); statement of the first main theorem 4. Automorphic vector bundles 5. Conjugates of automorphic vector bundles 6. Proof of Theorem 3.10 for the symplectic group 7. Proof of Theorem 3.10 for connected Shimura varieties of abelian type 8. First completion of the proof of Theorem 3.10 9. Second completion of the proof of Theorem 3.10 Appendix: Pairs defining connected and nonconnected Shimura varieties Bibliography 91 93 95 101 105 112 115 118 121 123 124 126 128