LEADER 00000cam a2200781Ka 4500 
001    ocn836848758 
003    OCoLC 
005    20190405013910.6 
006    m     o  d         
007    cr cnu---unuuu 
008    130408s2008    enka    ob    001 0 eng d 
019    704518046|a776967037|a843203457 
020    9781107363069|q(electronic bk.) 
020    1107363063|q(electronic bk.) 
020    9780511894046|q(e-book) 
020    051189404X|q(e-book) 
020    9780511721281|q(ebook) 
020    0511721285|q(ebook) 
020    9781107367975 
020    1107367972 
020    |z9780521728669 
020    |z0521728665 
035    (OCoLC)836848758|z(OCoLC)704518046|z(OCoLC)776967037
       |z(OCoLC)843203457 
040    N$T|beng|epn|cN$T|dE7B|dIDEBK|dOCLCF|dYDXCP|dAUD|dUUS
       |dMERUC|dMHW|dDEBSZ|dOCLCQ|dAU@ 
049    RIDW 
050  4 QA567.2.E44|bD36 2008eb 
072  7 MAT|x012010|2bisacsh 
082 04 516.3/52|222 
084    MAT 143f|2stub 
084    MAT 145f|2stub 
084    SK 180|2rvk 
084    SK 200|2rvk 
084    SI 320|2rvk 
090    QA567.2.E44|bD36 2008eb 
100 1  Delbourgo, Daniel. 
245 10 Elliptic curves and big Galois representations /|cDaniel 
       Delbourgo. 
260    Cambridge, UK ;|aNew York :|bCambridge University Press,
       |c2008. 
300    1 online resource (ix, 281 pages) :|billustrations. 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
490 1  London Mathematical Society lecture note series ;|v356 
504    Includes bibliographical references (pages 275-279) and 
       index. 
505 0  Cover; 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 (<U+007a>,
       <U+0044>)-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  3.2 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 <U+004e>-
       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  6.2 A two-variable interpolation6.3 Applications to 
       Iwasawa theory; 6.4 The Coleman exact sequence; 6.5 
       Computing the R[[<U+0044>]]-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  10.6 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. 
520 1  "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  Print version record. 
590    eBooks on EBSCOhost|bEBSCO eBook Subscription Academic 
       Collection - North America 
650  0 Curves, Elliptic. 
650  0 Galois theory. 
655  4 Electronic books. 
776 08 |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 London Mathematical Society lecture note series ;|v356. 
856 40 |uhttps://rider.idm.oclc.org/login?url=http://
       search.ebscohost.com/login.aspx?direct=true&scope=site&
       db=nlebk&AN=552371|zOnline eBook via EBSCO. Access 
       restricted to current Rider University students, faculty, 
       and staff. 
856 42 |3Instructions for reading/downloading the EBSCO version 
       of this eBook|uhttp://guides.rider.edu/ebooks/ebsco 
948    |d20190507|cEBSCO|tEBSCOebooksacademic NEW 4-5-19 7552
       |lridw 
994    92|bRID