Kolyvagin Systems.

Intro -- Contents -- Introduction -- 0.1. Selmer sheaves and Kolyvagin systems -- 0.2. Resemblance to the leading term of an L-function -- 0.3. Applications -- 0.4. Layout of the paper -- 0.5. Notation -- 0.6. Acknowledgments -- Chapter 1. Local Cohomology Groups -- 1.1. Local conditions -- 1.2. The finite/singular homomorphism -- 1.3. Local duality -- Chapter 2. Global Cohomology Groups and Selmer Structures -- 2.1. Selmer modules -- 2.2. Comparing Selmer modules -- 2.3. Global duality -- Chapter 3. Kolyvagin Systems -- 3.1. Kolyvagin systems -- 3.2. Euler systems and Kolyvagin systems -- 3.3. Simplicial sheaves and Selmer groups -- 3.4. Sheaves and monodromy -- 3.5. Hypotheses on T,F, and p -- 3.6. Choosing useful primes -- 3.7. Some remarks about hypothesis ( H.6) -- Chapter 4. Kolyvagin Systems over Principal Artinian Rings -- 4.1. The core Selmer module -- 4.2. Kolyvagin systems and the core rank -- 4.3. The sheaf of stub Selmer modules -- 4.4. Kolyvagin systems and the stub Selmer sheaf -- 4.5. Kolyvagin systems over principal artinian rings -- Chapter 5. Kolyvagin Systems over Integral Domains -- 5.1. Kolyvagin systems over a field -- 5.2. Kolyvagin systems over a discrete valuation ring -- 5.3. Kolyvagin systems over A -- Chapter 6. Examples -- 6.1. The multiplicative group -- 6.2. Elliptic curves -- 6.3. The multiplicative group, revisited -- Appendix A. Proof of Theorem 3.2.4 -- Appendix B. Proof of Theorem 4.3.3 -- Bibliography.

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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.