LEADER 05116nam 2200709Ia 450 001 9910792233803321 005 20230828232925.0 010 $a1-280-90406-2 010 $a9786610904068 010 $a0-19-151387-3 010 $a1-4294-6994-3 035 $a(CKB)2560000000296356 035 $a(EBL)3052127 035 $a(OCoLC)922952831 035 $a(SSID)ssj0000087327 035 $a(PQKBManifestationID)11126410 035 $a(PQKBTitleCode)TC0000087327 035 $a(PQKBWorkID)10054546 035 $a(PQKB)11651556 035 $a(StDuBDS)EDZ0000073182 035 $a(MiAaPQ)EBC3052127 035 $a(Au-PeEL)EBL3052127 035 $a(CaPaEBR)ebr10167530 035 $a(CaONFJC)MIL90406 035 $a(EXLCZ)992560000000296356 100 $a20060221d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHilbert modular forms and Iwasawa theory$b[electronic resource] /$fHaruzo Hida 210 $aOxford $cClarendon$d2006 215 $a1 online resource (417 p.) 225 1 $aOxford mathematical monographs 300 $aDescription based upon print version of record. 311 $a0-19-857102-X 311 $a0-19-171894-7 320 $aIncludes bibliographical references and index. 327 $aContents; 1 Introduction; 1.1 Classical Iwasawa theory; 1.1.1 Galois theoretic interpretation of the class group; 1.1.2 The Iwasawa algebra as a deformation ring; 1.1.3 Pseudo-representations; 1.1.4 Two-dimensional universal deformations; 1.2 Selmer groups; 1.2.1 Deligne's rationality conjecture; 1.2.2 Ordinary Galois representations; 1.2.3 Greenberg's Selmer groups; 1.2.4 Selmer groups with general coefficients; 1.3 Deformation and adjoint square Selmer groups; 1.3.1 Nearly ordinary deformation rings; 1.3.2 Adjoint square Selmer groups and differentials 327 $a1.3.3 Universal deformation rings are noetherian1.3.4 Elliptic modularity at a glance; 1.4 Iwasawa theory for deformation rings; 1.4.1 Galois action on deformation rings; 1.4.2 Control of adjoint square Selmer groups; 1.4.3 ?-adic forms; 1.5 Adjoint square L-invariants; 1.5.1 Balanced Selmer groups; 1.5.2 Greenberg's L-invariant; 1.5.3 Proof of Theorem 1.80; 2 Automorphic forms on inner forms of GL(2); 2.1 Quaternion algebras over a number field; 2.1.1 Quaternion algebras; 2.1.2 Orders of quaternion algebras; 2.2 A short review of algebraic geometry; 2.2.1 Affine schemes 327 $a2.2.2 Affine algebraic groups2.2.3 Schemes; 2.3 Automorphic forms on quaternion algebras; 2.3.1 Arithmetic quotients; 2.3.2 Archimedean Hilbert modular forms; 2.3.3 Hilbert modular forms with integral coefficients; 2.3.4 Duality and Hecke algebras; 2.3.5 Quaternionic automorphic forms; 2.3.6 The Jacquet-Langlands correspondence; 2.3.7 Local representations of GL(2); 2.3.8 Modular Galois representations; 2.4 The integral Jacquet-Langlands correspondence; 2.4.1 Classical Hecke operators; 2.4.2 Hecke algebras; 2.4.3 Cohomological correspondences; 2.4.4 Eichler-Shimura isomorphisms 327 $a2.5 Theta series2.5.1 Quaternionic theta series; 2.5.2 Siegel's theta series; 2.5.3 Transformation formulas; 2.5.4 Theta series of imaginary quadratic fields; 2.6 The basis problem of Eichler; 2.6.1 The elliptic Jacquet-Langlands correspondence; 2.6.2 Eichler's integral correspondence; 3 Hecke algebras as Galois deformation rings; 3.1 Hecke algebras; 3.1.1 Automorphic forms on definite quaternions; 3.1.2 Hecke operators; 3.1.3 Inner products; 3.1.4 Ordinary Hecke algebras; 3.1.5 Automorphic forms of higher weight; 3.2 Galois deformation; 3.2.1 Minimal deformation problems 327 $a3.2.2 Tangent spaces of local deformation functors3.2.3 Taylor-Wiles systems; 3.2.4 Hecke algebras are universal; 3.2.5 Flat deformations; 3.2.6 Freeness over the Hecke algebra; 3.2.7 Hilbert modular basis problems; 3.2.8 Locally cyclotomic deformation; 3.2.9 Locally cyclotomic Hecke algebras; 3.2.10 Global deformation over a p-adic field; 3.3 Base change; 3.3.1 p-Ordinary Jacquet-Langlands correspondence; 3.3.2 Base fields of odd degree; 3.3.3 Automorphic base change; 3.3.4 Galois base change; 3.4 L-invariants of Hilbert modular forms; 3.4.1 Statement of the result 327 $a3.4.2 Deformation without monodromy conditions 330 8 $aDescribing the applications found for the Wiles and Taylor technique, this book generalizes the deformation theoretic techniques of Wiles-Taylor to Hilbert modular forms (following Fujiwara's treatment), and also discusses applications found by the author. 410 0$aOxford mathematical monographs. 606 $aForms, Modular 606 $aHilbert modular surfaces 606 $aIwasawa theory 615 0$aForms, Modular. 615 0$aHilbert modular surfaces. 615 0$aIwasawa theory. 676 $a512.74 700 $aHida$b Haruzo$062786 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910792233803321 996 $aHilbert modular forms and Iwasawa theory$91099247 997 $aUNINA