000 | 06596cam a2200865 a 4500 | ||
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001 | ocn836848758 | ||
003 | OCoLC | ||
005 | 20220711194907.0 | ||
006 | m o d | ||
007 | cr cnu---unuuu | ||
008 | 130408s2008 enka ob 001 0 eng d | ||
040 |
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_aMAT 145f _2stub |
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084 |
_aMAT 143f _2stub |
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049 | _aMAIN | ||
100 | 1 |
_aDelbourgo, Daniel. _9937359 |
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245 | 1 | 0 |
_aElliptic curves and big Galois representations / _cDaniel Delbourgo. |
260 |
_aCambridge, UK ; _aNew York : _bCambridge University Press, _c2008. |
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300 |
_a1 online resource (ix, 281 pages) : _billustrations |
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336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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490 | 1 |
_aLondon Mathematical Society lecture note series ; _v356 |
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504 | _aIncludes bibliographical references (pages 275-279) and index. | ||
520 | 1 | _a"The mysterious properties of modular forms lie at the heart of modern number theory. This book develops a generalisation of the method of Euler systems to a two-variable deformation ring. The resulting theory is then used to study the arithmetic of elliptic curves, in particular the Birch and Swinnerton-Dyer (BSD) formula." "Three main steps are outlined. The first is to parametrise 'big' cohomology groups using (deformations of) modular symbols. One can then establish finiteness results for big Selmer groups. Finally, at weight two, the arithmetic invariants of these Selmer groups allow the control of data from the BSD conjecture." "This is the first book on the subject, and the material is introduced from scratch; both graduate students and professional number theorists will find this an ideal introduction to the subject. Material at the very forefront of current research is included, and numerical examples encourage the reader to interpret abstract theorems in concrete cases."--Jacket | |
588 | 0 | _aPrint version record. | |
505 | 0 | _aCover; Title; Copyright; Dedication; Contents; Introduction; List of Notations; Chapter I Background; 1.1 Elliptic curves; 1.2 Hasse-Weil L-functions; 1.3 Structure of the Mordell-Weil group; 1.4 The conjectures of Birch and Swinnerton-Dyer; 1.5 Modular forms and Hecke algebras; Chapter II p-Adic L-functions and Zeta Elements; 2.1 The p-adic Birch and Swinnerton-Dyer conjecture; 2.2 Perrin-Riou's local Iwasawa theory; 2.3 Integrality and (z, D)-modules; 2.4 Norm relations in K-theory; 2.5 Kato's p-adic zeta-elements; Chapter III Cyclotomic Deformations of Modular Symbols; 3.1 Q-continuity. | |
505 | 8 | _a3.2 Cohomological subspaces of Euler systems3.3 The one-variable interpolation; 3.4 Local freeness of the image; Chapter IV A User's Guide to Hida Theory; 4.1 The universal ordinary Galois representation; 4.2 N-adic modular forms; 4.3 Multiplicity one for I-adic modular symbols; 4.4 Two-variable p-adic L-functions; Chapter V Crystalline Weight Deformations; 5.1 Cohomologies over deformation rings; 5.2 p-Ordinary deformations of Bcris and Dcris; 5.3 Constructing big dual exponentials; 5.4 Local dualities; Chapter VI Super Zeta-Elements; 6.1 The R-adic version of Kato's theorem. | |
505 | 8 | _a6.2 A two-variable interpolation6.3 Applications to Iwasawa theory; 6.4 The Coleman exact sequence; 6.5 Computing the R[[D]]-torsion; Chapter VII Vertical and Half-Twisted Arithmetic; 7.1 Big Selmer groups; 7.2 The fundamental commutative diagrams; 7.3 Control theory for Selmer coranks; Chapter VIII Diamond-Euler Characteristics: the Local Case; 8.1 Analytic rank zero; 8.2 The Tamagawa factors away from p; 8.3 The Tamagawa factors above p (the vertical case); 8.4 The Tamagawa factors above p (the half-twisted case); 8.5 Evaluating the covolumes. | |
505 | 8 | _a10.6 Numerical examples, open problemsAppendices; A: The Primitivity of Zeta Elements; B: Specialising the Universal Path Vector; C: The Weight-Variable Control Theorem (by Paul A. Smith); C.1 Notation and assumptions; C.2 Properties of affinoids; C.3 The cohomology of a lattice L; C.4 Local conditions; C.5 Dualities via the Ext-pairings; C.6 Controlling the Selmer groups; Bibliography; Index. | |
590 |
_aeBooks on EBSCOhost _bEBSCO eBook Subscription Academic Collection - Worldwide |
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650 | 0 |
_aCurves, Elliptic. _9162527 |
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650 | 0 |
_aGalois theory. _9288332 |
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650 | 6 |
_aCourbes elliptiques. _9869417 |
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650 | 6 |
_aThéorie de Galois. _9937360 |
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650 | 7 |
_aMATHEMATICS _xGeometry _xAlgebraic. _2bisacsh _9869419 |
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650 | 7 |
_aCurves, Elliptic. _2fast _0(OCoLC)fst00885455 _9162527 |
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650 | 7 |
_aGalois theory. _2fast _0(OCoLC)fst00937326 _9288332 |
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650 | 7 |
_aElliptische Kurve _2gnd _9937361 |
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650 | 7 |
_aGalois-Darstellung _2gnd _9937362 |
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655 | 4 | _aElectronic books. | |
776 | 0 | 8 |
_iPrint version: _aDelbourgo, Daniel. _tElliptic curves and big Galois representations. _dCambridge, UK ; New York : Cambridge University Press, 2008 _z9780521728669 _w(DLC) 2008021192 _w(OCoLC)227275650 |
830 | 0 |
_aLondon Mathematical Society lecture note series ; _v356. _9144795 |
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856 | 4 | 0 | _uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552371 |
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