LEADER 03061nam 2200589 450 001 996466538603316 005 20220821135340.0 010 $a3-540-38854-0 024 7 $a10.1007/BFb0082111 035 $a(CKB)1000000000437501 035 $a(SSID)ssj0000321393 035 $a(PQKBManifestationID)12116012 035 $a(PQKBTitleCode)TC0000321393 035 $a(PQKBWorkID)10279842 035 $a(PQKB)11320269 035 $a(DE-He213)978-3-540-38854-8 035 $a(MiAaPQ)EBC5595418 035 $a(Au-PeEL)EBL5595418 035 $a(OCoLC)1076233237 035 $a(MiAaPQ)EBC6812111 035 $a(Au-PeEL)EBL6812111 035 $a(OCoLC)1287129415 035 $a(PPN)155173227 035 $a(EXLCZ)991000000000437501 100 $a20220821d1988 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aArithmetic of p-adic modular forms /$fFernando Q. Gouve?a 205 $a1st ed. 1988. 210 1$aBerlin, Heidelberg :$cSpringer-Verlag,$d[1988] 210 4$dİ1988 215 $a1 online resource (X, 122 p.) 225 1 $aLecture Notes in Mathematics ;$v1304 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-18946-7 327 $aContents: p-adic Modular Forms: Level Structures and Trivializations. p-adic Modular Forms with Growth Conditions. Generalized p-adic Modular Functions -- Hecke and U Operators: Hecke Operators. The Frobenius Operator. The U Operator. Appendix: Hida's Theory of the Ordinary Part -- Galois Representations: Duality Theorems. Families of Modular Forms. Changing the Level. Deformations of Residual Eigenforms. Deformations of Galois Representations. The Modular Deformation Space. Further Questions. 330 $aThe central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject. 410 0$aLecture notes in mathematics ;$v1304. 606 $aForms, Modular 615 0$aForms, Modular. 676 $a512.73 700 $aGouve?a$b Fernando Q$g(Fernando Quadros),$0382239 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466538603316 996 $aArithmetic of p-adic modular forms$9381139 997 $aUNISA