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101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aKolyvagin systems /$fBarry Mazur, Karl Rubin
210  1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2004.
210  4$dİ2004
215   $a1 online resource (112 p.)
225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 168, Number 799
300   $a"March 2004, Volume 168, Number 799 (end of volume)."
311   $a0-8218-3512-2 
320   $aIncludes bibliographical references.
327   $a""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""
327   $a""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""
327   $a""5.1. Kolyvagin systems over a field""""5.2. Kolyvagin systems over a discrete valuation ring""; ""5.3. Kolyvagin systems over A""; ""Chapter 6. Examples""; ""6.1. The multiplicative group""; ""6.2. Elliptic curves""; ""6.3. The multiplicative group, revisited""; ""Appendix A. Proof of Theorem 3.2.4""; ""Appendix B. Proof of Theorem 4.3.3""; ""Bibliography""
410  0$aMemoirs of the American Mathematical Society ;$vVolume 168, Number 799.
606   $aBirch-Swinnerton-Dyer conjecture
606   $aL-functions
606   $aArithmetical algebraic geometry
608   $aElectronic books.
615  0$aBirch-Swinnerton-Dyer conjecture.
615  0$aL-functions.
615  0$aArithmetical algebraic geometry.
676   $a516.3/5
700   $aMazur$b Barry$0441265
702   $aRubin$b Karl
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910478885603321
996   $aKolyvagin systems$91989028
997   $aUNINA