CMI SUMMER SCHOOL NOTES ON p - ADIC HODGE THEORY ( PRELIMINARY VERSION )
نویسنده
چکیده
Part I. First steps in p-adic Hodge theory 4 1. Motivation 4 1.1. Tate modules 4 1.2. Galois lattices and Galois deformations 6 1.3. Aims of p-adic Hodge theory 7 1.4. Exercises 9 2. Hodge–Tate representations 10 2.1. Basic properties of CK 11 2.2. Theorems of Tate–Sen and Faltings 12 2.3. Hodge–Tate decomposition 15 2.4. Formalism of Hodge–Tate representations 17 2.5. Exercises 24 3. Étale φ-modules 26 3.1. p-torsion representations 26 3.2. Torsion and lattice representations 31 3.3. Qp-representations of GE 41 3.4. Exercises 42 4. Better ring-theoretic constructions 44 4.1. From gradings to filtrations 44 4.2. Witt vectors and universal Witt constructions 47 4.3. Properties of R 51 4.4. The field of p-adic periods BdR 55 4.5. Exercises 65 5. Formalism of admissible representations 67 5.1. Definitions and examples 67 5.2. Properties of admissible representations 68 5.3. Exercises 73
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