| Acknowledgments | p. xi |
| Introduction | p. 3 |
| Notation | p. 6 |
| Galois Cohomology of p-adic Representations | p. 9 |
| p-adic Representations | p. 9 |
| Galois Cohomology | p. 11 |
| Local Cohomology Groups | p. 12 |
| Local Duality | p. 18 |
| Global Cohomology Groups | p. 21 |
| Examples of Selmer Groups | p. 23 |
| Global Duality | p. 28 |
| Euler Systems: Definition and Main Results | p. 33 |
| Euler Systems | p. 33 |
| Results over K | p. 36 |
| Results over K,, | p. 40 |
| Twisting by Characters of Finite Order | p. 43 |
| Examples and Applications | p. 47 |
| Preliminaries | p. 47 |
| Cyclotomic Units | p. 48 |
| Elliptic Units | p. 55 |
| Stickelberger Elements | p. 55 |
| Elliptic Curves | p. 63 |
| Symmetric Square of an Elliptic Curve | p. 73 |
| Derived Cohomology Classes | p. 75 |
| Setup | p. 75 |
| The Universal Euler System | p. 78 |
| Properties of the Universal Euler System | p. 80 |
| Kolyvagin's Derivative Construction | p. 83 |
| Local Properties of the Derivative Classes | p. 90 |
| Local Behavior at Primes Not Dividing pr | p. 92 |
| Local Behavior at Primes Dividing r | p. 98 |
| The Congruence | p. 102 |
| Bounding the Selmer Group | p. 105 |
| Preliminaries | p. 105 |
| Bounding the Order of the Selmer Group | p. 106 |
| Bounding the Exponent of the Selmer Group | p. 114 |
| Twisting | p. 119 |
| Twisting Representations | p. 119 |
| Twisting Cohomology Groups | p. 121 |
| Twisting Euler Systems | p. 122 |
| Twisting Theorems | p. 125 |
| Examples and Applications | p. 125 |
| Iwasawa, Theory | p. 129 |
| Overview | p. 129 |
| Galois Groups and the Evaluation Map | p. 135 |
| Proof of Theorem 2.3.2 | p. 141 |
| The Kernel and Cokernel of the Restriction Map | p. 145 |
| Galois Equivariance of the Evaluation Maps | p. 147 |
| Proof of Proposition 7.1.7 | p. 151 |
| Proof of Proposition 7.1.9 | p. 154 |
| Euler Systems and p-adic L-functions | p. 163 |
| The Setting | p. 164 |
| Perrin-Riou's p-adic L-function and Related Conjectures | p. 166 |
| Connection with Euler Systems when d- = 1 | p. 168 |
| Example: Cyclotomic Units | p. 171 |
| Connection with Euler Systems when d- >1 | p. 173 |
| Variants | p. 175 |
| Rigidity | p. 175 |
| Finite Primes Splitting Completely in K,,,IK | p. 178 |
| Euler Systems of Finite Depth | p. 179 |
| Anticyclotomic Euler Systems | p. 180 |
| Additional Local Conditions | p. 183 |
| Varying the Euler Factors | p. 185 |
| Linear Algebra | p. 189 |
| Herbrand Quotients | p. 189 |
| p-adic Representations | p. 191 |
| Continuous Cohomology and Inverse Limits | p. 195 |
| Preliminaries | p. 195 |
| Continuous Cohomology | p. 195 |
| Inverse Limits | p. 198 |
| Induced Modules | p. 201 |
| Semilocal Galois Cohomology | p. 202 |
| Cohomology of p-adic Analytic Groups | p. 205 |
| Irreducible Actions of Compact Groups | p. 205 |
| Application to Galois Representations | p. 207 |
| p-adic Calculations in Cyclotomic Fields | p. 211 |
| Local Units in Cyclotomic Fields | p. 211 |
| Cyclotomic Units | p. 216 |
| Bibliography | p. 219 |
| Index of Symbols | p. 223 |
| Subject Index | p. 227 |
| Table of Contents provided by Publisher. All Rights Reserved. |
