000 03119nam a22004815i 4500
001 978-3-540-38854-8
003 DE-He213
005 20190213151151.0
007 cr nn 008mamaa
008 121227s1988 gw | s |||| 0|eng d
020 _a9783540388548
_9978-3-540-38854-8
024 7 _a10.1007/BFb0082111
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
072 7 _aPBH
_2thema
082 0 4 _a512.7
_223
100 1 _aGouvêa, Fernando Quadros.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aArithmetic of p-adic Modular Forms
_h[electronic resource] /
_cby Fernando Quadros Gouvêa.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1988.
300 _aX, 122 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1304
505 0 _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.
520 _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.
650 0 _aNumber theory.
650 0 _aGeometry, algebraic.
650 1 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662193846
776 0 8 _iPrinted edition:
_z9783540189466
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1304
856 4 0 _uhttps://doi.org/10.1007/BFb0082111
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9750
_d9750