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001 CR9780511526046
003 UkCbUP
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020 _a9780511526046 (ebook)
020 _z9780521770361 (hardback)
020 _z9780521072083 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA243
_b.H43 2000
082 0 0 _a512/.73
_221
100 1 _aHida, Haruzo,
_eauthor.
245 1 0 _aModular forms and Galois cohomology /
_cHaruzo Hida.
246 3 _aModular Forms & Galois Cohomology
264 1 _aCambridge :
_bCambridge University Press,
_c2000.
300 _a1 online resource (x, 343 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge studies in advanced mathematics ;
_v69
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 _g1.
_tOverview of Modular Forms.
_g1.1.
_tHecke Characters.
_g1.2.
_tIntroduction to Modular Forms --
_g2.
_tRepresentations of a Group.
_g2.1.
_tGroup Representations.
_g2.2.
_tPseudo-representations.
_g2.3.
_tDeformation of Group Representations --
_g3.
_tRepresentations of Galois Groups and Modular Forms.
_g3.1.
_tModular Forms on Adele Groups of GL(2).
_g3.2.
_tModular Galois Representations --
_g4.
_tCohomology Theory of Galois Groups.
_g4.1.
_tCategories and Functors.
_g4.2.
_tExtension of Modules.
_g4.3.
_tGroup Cohomology Theory.
_g4.4.
_tDuality in Galois Cohomology --
_g5.
_tModular L-Values and Selmer Groups.
_g5.1.
_tSelmer Groups.
_g5.2.
_tAdjoint Selmer Groups.
_g5.3.
_tArithmetic of Modular Adjoint L-Values.
_g5.4.
_tControl of Universal Deformation Rings.
520 _aThis book provides a comprehensive account of a key (and perhaps the most important) theory upon which the Taylor-Wiles proof of Fermat's last theorem is based. The book begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and results on elliptic modular forms, including a substantial simplification of the Taylor-Wiles proof by Fujiwara and Diamond. It contains a detailed exposition of the representation theory of profinite groups (including deformation theory), as well as the Euler characteristic formulas of Galois cohomology groups. The final chapter presents a proof of a non-abelian class number formula and includes several new results from the author. The book will be of interest to graduate students and researchers in number theory (including algebraic and analytic number theorists) and arithmetic algebraic geometry.
650 0 _aForms, Modular.
650 0 _aGalois theory.
650 0 _aHomology theory.
776 0 8 _iPrint version:
_z9780521770361
830 0 _aCambridge studies in advanced mathematics ;
_v69.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511526046
999 _c518302
_d518300