LEADER 04054nam 2200685 450 001 9910465328803321 005 20200520144314.0 010 $a0-691-05075-9 010 $a1-4008-6520-4 024 7 $a10.1515/9781400865208 035 $a(CKB)3710000000221859 035 $a(EBL)1756197 035 $a(OCoLC)887499496 035 $a(SSID)ssj0001378329 035 $a(PQKBManifestationID)11816897 035 $a(PQKBTitleCode)TC0001378329 035 $a(PQKBWorkID)11339924 035 $a(PQKB)10317839 035 $a(MiAaPQ)EBC1756197 035 $a(DE-B1597)448057 035 $a(OCoLC)891400001 035 $a(OCoLC)979954521 035 $a(DE-B1597)9781400865208 035 $a(Au-PeEL)EBL1756197 035 $a(CaPaEBR)ebr10907684 035 $a(CaONFJC)MIL636774 035 $a(EXLCZ)993710000000221859 100 $a20140822h20002000 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aEuler systems /$fby Karl Rubin 210 1$aPrinceton, New Jersey ;$aChichester, England :$cPrinceton University Press,$d2000. 210 4$dİ2000 215 $a1 online resource (241 p.) 225 1 $aAnnals of Mathematics Studies ;$vNumber 147 300 $aDescription based upon print version of record. 311 $a1-322-05523-8 311 $a0-691-05076-7 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tAcknowledgments /$rRubin, Karl --$tIntroduction --$tChapter 1. Galois Cohomology of p-adic Representations --$tChapter 2. Euler Systems: Definition and Main Results --$tChapter 3. Examples and Applications --$tChapter 4. Derived Cohomology Classes --$tChapter 5. Bounding the Selmer Group --$tChapter 6. Twisting --$tChapter 7. Iwasawa Theory --$tChapter 8. Euler Systems and p-adic L-functions --$tChapter 9. Variants --$tAppendix A. Linear Algebra --$tAppendix B. Continuous Cohomology and Inverse Limits --$tAppendix C. Cohomology of p-adic Analytic Groups --$tAppendix D. p-adic Calculations in Cyclotomic Fields --$tBibliography --$tIndex of Symbols --$tSubject Index 330 $aOne of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980's in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry. 410 0$aAnnals of mathematics studies ;$vNumber 147. 606 $aAlgebraic number theory 606 $ap-adic numbers 608 $aElectronic books. 615 0$aAlgebraic number theory. 615 0$ap-adic numbers. 676 $a512/.74 700 $aRubin$b Karl$059452 702 $aRubin$b Karl, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465328803321 996 $aEuler systems$9377969 997 $aUNINA