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LEADER: 05547cam a2200733Mu 4500
001 15131502
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006 m o d
007 cr |n|---|||||
008 180324s1997 xx ob 001 0 eng d
035 $a(OCoLC)on1029488604
035 $a(NNC)15131502
040 $aEBLCP$beng$epn$cEBLCP$dMERUC$dYDX$dN$T$dOCLCF$dOCLCQ$dUPM$dOCLCQ$dUKAHL$dOCLCO$dOCLCQ
019 $a1029318830$a1049858438$a1080587944$a1090790280$a1100684938
020 $a9781439863862
020 $a1439863865
020 $z1568810776
020 $z9781568810775
035 $a(OCoLC)1029488604$z(OCoLC)1029318830$z(OCoLC)1049858438$z(OCoLC)1080587944$z(OCoLC)1090790280$z(OCoLC)1100684938
050 4 $aQA176.S47 1997
072 7 $aMAT$x002040$2bisacsh
082 04 $a512/.7
084 $a*14G99$2msc
084 $a11G05$2msc
084 $a14-02$2msc
084 $a14H52$2msc
084 $a22E05$2msc
084 $aSK 240$2rvk
084 $aSK 180$2rvk
049 $aZCUA
100 1 $aSerre, Jean Pierre.
245 10 $aAbelian l-Adic Representations and Elliptic Curves.
250 $a3rd ed.
260 $aNatick :$bChapman and Hall/CRC,$c1997.
300 $a1 online resource (203 pages)
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
490 1 $aResearch Notes in Mathematics Ser. ;$vv. 7
588 0 $aPrint version record.
505 0 $aCover; Half Title; Title Page; Copyright Page; Special Preface; Preface; Vita; Table of Contents; INTRODUCTION; NOTATIONS; Chapter I: l-adic Representations; Â1 The notion of an l-adic representation; 1.1 Definition; 1.2 Examples; Â2 l-adic representations of number fields; 2.1 Preliminaries; 2.2 Cebotarev's density theorem; 2.3 Rationall-adic representations; 2.4 Representations with values in a linear algebraic group; 2.5 L-functions attached to rational representations; Appendix Equipartition and L-functions; A.1 Equipartition; A.2 The connection with L-functions; A.3 Proof of theorem 1.
505 8 $aChapter II: The Groups SmÂ1 Preliminaries; 1.1 The torus T; 1.2 Cutting down T; 1.3 Enlarging groups; Â2 Construction of Tm and Sm; 2.1 IdÃl̈es and idÃl̈e-classes; 2.2 The groups Tm and Sm; 2.3 The canonical l-adic representation with values in Sm; 2.4 Linear representations of Sm; 2.5 l-adic representations associated to a linear representation of Sm; 2.6 Alternative construction; 2.7 The real case; 2.8 An example: complex multiplication of abelian varieties; Â3 Structure of Tm and applications; 3.1 Structure of X(Tm); 3.2 The morphism j* : Gm â#x86;#x92; Tm; 3.3 Structure of Tm.
505 8 $a3.4 How to compute FrobeniusesAppendix Killing arithmetic groups in tori; A.1 Arithmetic groups in tori; A.2 Killing arithmetic subgroups; Chapter Ill: Locally Algebraic Abelian Representations; Â1 The local case; 1.1 Definitions; 1.2 Alternative definition of ""locally algebraic"" via Hodge-Tate modules; Â2 The global case; 2.1 Definitions; 2.2 Modulus of a locally algebraic abelian representation; 2.3 Back to Sm; 2.4 A mild generalization; 2.5 The function field case; Â3 The case of a composite of quadratic fields; 3.1 Statement of the result; 3.2 A criterion for local algebraicity.
505 8 $a3.3 An auxiliary result on tori3.4 Proof of the theorem; Appendix Hodge-Tate decompositions and locally algebraic representations; A.1 lnvariance of Hodge-Tate decompositions; A.2 Admissible characters; A.3 A criterion for local triviality; A.4 The character ÎℓE; A.5 Characters associated with Hodge-Tate decompositions; A.6 Locally compact case; A.7 Tate's theorem; Chapter IV: l-adic Representations Attached to Elliptic Curves; Â1 Preliminaries; 1.1 Elliptic curves; 1.2 Good reduction; 1.3 Properties of V1 related to good reduction; 1.4 SafareviÄ#x8D;' s theorem.
505 8 $aÂ2 The Galois modules attached to E2.1 The irreducibility theorem; 2.2 Determination of the Lie algebra of G1; 2.3 The isogeny theorem; Â3 Variation of Gl and GÌ#x83;l with l; 3.1 Preliminaries; 3.2 The case of a non integral j; 3.3 Numerical example; 3.4 Proof of the main lemma of 3.1; Appendix Local results; A.1 The case v(j) <0; A.1.1. The elliptic curves of Tate; A.1.2 An exact sequence; A.1.4 Application to isogenies; A.1.5 Existence of transvections in the inertia group; A.2 The case v(j) â#x89;Æ 0; A.2.1 The case 1 â#x89; p; A.2.2 The case 1 = p with good reduction of height 2.
500 $aA.2.3 Auxiliary results on abelian varieties.
504 $aIncludes bibliographical references and index.
650 0 $aRepresentations of groups.
650 0 $aCurves, Elliptic.
650 0 $aAlgebraic fields.
650 6 $aReprésentations de groupes.
650 6 $aCourbes elliptiques.
650 6 $aCorps algébriques.
650 7 $aMATHEMATICS$xAlgebra$xIntermediate.$2bisacsh
650 7 $aAlgebraic fields.$2fast$0(OCoLC)fst00804931
650 7 $aCurves, Elliptic.$2fast$0(OCoLC)fst00885455
650 7 $aRepresentations of groups.$2fast$0(OCoLC)fst01094938
650 7 $aElliptische Kurve$2gnd
650 7 $aKommutative Algebra$2gnd
655 4 $aElectronic books.
776 08 $iPrint version:$aSerre, Jean Pierre.$tAbelian l-Adic Representations and Elliptic Curves.$dNatick : Chapman and Hall/CRC, ©1997$z9781568810775
830 0 $aResearch Notes in Mathematics Ser.
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio15131502$zTaylor & Francis eBooks
852 8 $blweb$hEBOOKS