viii CONTENTS
4.3. Tensor construction for p-divisible groups 224
4.4. Self-duality and CM lifting 228
4.5. Striped and supersingular Lie types 233
4.6. Complex conjugation and CM lifting 240
Appendix A. Some arithmetic results for abelian varieties 249
A.1. The p-part of Tate’s work 249
A.2. The Main Theorem of Complex Multiplication 257
A.3. A converse to the Main Theorem of Complex Multiplication 292
A.4. Existence of algebraic Hecke characters 296
Appendix B. CM lifting via p-adic Hodge theory 321
B.1. A generalization of the toy model 321
B.2. Construct CM lifting by p-adic Hodge theory 333
B.3. Dieudonn´ e theories over a perfect field of characteristic p 343
B.4. p-adic Hodge theory and a formula for the closed fiber 359
Notes on Quotes 371
Glossary of Notations 373
Bibliography 379
Index 385
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