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007    cr cnu---unuuu 
008    130408s2008    enka    ob    001 0 eng d 
019    704518046|a776967037|a843203457 
020    9781107363069|q(electronic book) 
020    1107363063|q(electronic book) 
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
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040    N$T|beng|epn|cN$T|dE7B|dIDEBK|dOCLCF|dYDXCP|dAUD|dUUS
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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.|0https://id.loc.gov/authorities/names/
       n2008034277 
245 10 Elliptic curves and big Galois representations /|cDaniel 
       Delbourgo. 
264  1 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 
340    |gpolychrome|2rdacc 
347    text file|2rdaft 
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 (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  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 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  6.2 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  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.|0https://id.loc.gov/authorities/subjects
       /sh85034918 
650  0 Galois theory.|0https://id.loc.gov/authorities/subjects/
       sh85052872 
650  7 Curves, Elliptic.|2fast|0https://id.worldcat.org/fast/
       885455 
650  7 Galois theory.|2fast|0https://id.worldcat.org/fast/937326 
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 ;|0https:/
       /id.loc.gov/authorities/names/n42015587|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 
901    MARCIVE 20231220 
948    |d20190507|cEBSCO|tEBSCOebooksacademic NEW 4-5-19 7552
       |lridw 
994    92|bRID