Euler Systems. (AM-147), Volume 147.

Cover -- Title -- Copyright -- Contents -- Acknowledgments -- Introduction -- Notation -- Chapter 1. Galois Cohomology of p-adic Representations -- 1.1. p-adic Representations -- 1.2. Galois Cohomology -- 1.3. Local Cohomology Groups -- 1.4. Local Duality -- 1.5. Global Cohomology Groups -- 1.6. Examples of Selmer Groups -- 1.7. Global Duality -- Chapter 2. Euler Systems: Definition and Main Results -- 2.1. Euler Systems -- 2.2. Results over K -- 2.3. Results over K∞ -- 2.4. Twisting by Characters of Finite Order -- Chapter 3. Examples and Applications -- 3.1. Preliminaries -- 3.2. Cyclotomic Units -- 3.3. Elliptic Units -- 3.4. Stickelberger Elements -- 3.5. Elliptic Curves -- 3.6. Symmetric Square of an Elliptic Curve -- Chapter 4. Derived Cohomology Classes -- 4.1. Setup -- 4.2. The Universal Euler System -- 4.3. Properties of the Universal Euler System -- 4.4. Kolyvagin's Derivative Construction -- 4.5. Local Properties of the Derivative Classes -- 4.6. Local Behavior at Primes Not Dividing pτ -- 4.7. Local Behavior at Primes Dividing τ -- 4.8. The Congruence -- Chapter 5. Bounding the Selmer Group -- 5.1. Preliminaries -- 5.2. Bounding the Order of the Selmer Group -- 5.3. Bounding the Exponent of the Selmer Group -- Chapter 6. Twisting -- 6.1. Twisting Representations -- 6.2. Twisting Cohomology Groups -- 6.3. Twisting Euler Systems -- 6.4. Twisting Theorems -- 6.5. Examples and Applications -- Chapter 7. Iwasawa Theory -- 7.1. Overview -- 7.2. Galois Groups and the Evaluation Map -- 7.3. Proof of Theorem 2.3.2 -- 7.4. The Kernel and Cokernel of the Restriction Map -- 7.5. Galois Equivariance of the Evaluation Maps -- 7.6. Proof of Proposition 7.1.7 -- 7.7. Proof of Proposition 7.1.9 -- Chapter 8. Euler Systems and p-adic L-functions -- 8.1. The Setting -- 8.2. Perrin-Riou's p-adic L-function and Related Conjectures.

8.3. Connection with Euler Systems when d_ = 1 -- 8.4. Example: Cyclotomic Units -- 8.5. Connection with Euler Systems when d_ &gt -- 1 -- Chapter 9. Variants -- 9.1. Rigidity -- 9.2. Finite Primes Splitting Completely in K∞/ K -- 9.3. Euler Systems of Finite Depth -- 9.4. Anticyclotomic Euler Systems -- 9.5. Additional Local Conditions -- 9.6. Varying the Euler Factors -- Appendix A. Linear Algebra -- A.1. Herbrand Quotients -- A.2. p-adic Representations -- Appendix B. Continuous Cohomology and Inverse Limits -- B.1. Preliminaries -- B.2. Continuous Cohomology -- B.3. Inverse Limits -- B.4. Induced Modules -- B.5. Semilocal Galois Cohomology -- Appendix C. Cohomology of p-adic Analytic Groups -- C.1. Irreducible Actions of Compact Groups -- C.2. Application to Galois Representations -- Appendix D. p-adic Calculations in Cyclotomic Fields -- D.1. Local Units in Cyclotomic Fields -- D.2. Cyclotomic Units -- Bibliography -- Index of Symbols -- Subject Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.