000 02281nam a22003618i 4500
001 CR9780511721281
003 UkCbUP
005 20200124160239.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 100303s2008||||enk o ||1 0|eng|d
020 _a9780511721281 (ebook)
020 _z9780521728669 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA567.2.E44
_bD36 2008
082 0 0 _a516.3/52
_222
100 1 _aDelbourgo, Daniel,
_eauthor.
245 1 0 _aElliptic curves and big Galois representations /
_cDaniel Delbourgo.
246 3 _aElliptic Curves & Big Galois Representations
264 1 _aCambridge :
_bCambridge University Press,
_c2008.
300 _a1 online resource (ix, 281 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aLondon Mathematical Society lecture note series ;
_v356
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
520 _aThe arithmetic properties of modular forms and elliptic curves 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. Finiteness results for big Selmer groups are then established. Finally, at weight two, the arithmetic invariants of these Selmer groups allow the control of data from the BSD conjecture. As the first book on the subject, the material is introduced from scratch; both graduate students and professional number theorists will find this an ideal introduction. Material at the very forefront of current research is included, and numerical examples encourage the reader to interpret abstract theorems in concrete cases.
650 0 _aCurves, Elliptic.
650 0 _aGalois theory.
776 0 8 _iPrint version:
_z9780521728669
830 0 _aLondon Mathematical Society lecture note series ;
_v356.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511721281
999 _c518361
_d518359