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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
610   $aAbelian extension.
610   $aAbelian variety.
610   $aAbsolute Galois group.
610   $aAlgebraic closure.
610   $aBarry Mazur.
610   $aBig O notation.
610   $aBirch and Swinnerton-Dyer conjecture.
610   $aCardinality.
610   $aClass field theory.
610   $aCoefficient.
610   $aCohomology.
610   $aComplex multiplication.
610   $aConjecture.
610   $aCorollary.
610   $aCyclotomic field.
610   $aDimension (vector space).
610   $aDivisibility rule.
610   $aEigenvalues and eigenvectors.
610   $aElliptic curve.
610   $aError term.
610   $aEuler product.
610   $aEuler system.
610   $aExact sequence.
610   $aExistential quantification.
610   $aField of fractions.
610   $aFinite set.
610   $aFunctional equation.
610   $aGalois cohomology.
610   $aGalois group.
610   $aGalois module.
610   $aGauss sum.
610   $aGlobal field.
610   $aHeegner point.
610   $aIdeal class group.
610   $aInteger.
610   $aInverse limit.
610   $aInverse system.
610   $aKarl Rubin.
610   $aLocal field.
610   $aMathematical induction.
610   $aMaximal ideal.
610   $aModular curve.
610   $aModular elliptic curve.
610   $aNatural number.
610   $aOrthogonality.
610   $aP-adic number.
610   $aPairing.
610   $aPrincipal ideal.
610   $aR-factor (crystallography).
610   $aRalph Greenberg.
610   $aRemainder.
610   $aResidue field.
610   $aRing of integers.
610   $aScientific notation.
610   $aSelmer group.
610   $aSubgroup.
610   $aTate module.
610   $aTaylor series.
610   $aTensor product.
610   $aTheorem.
610   $aUpper and lower bounds.
610   $aVictor Kolyvagin.
615  0$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   $a9910816804403321
996   $aEuler systems$9377969
997   $aUNINA