Automorphic Forms and Galois Representations: Volume 1 PDF
Preview Automorphic Forms and Galois Representations: Volume 1
LONDONMATHEMATICALSOCIETYLECTURENOTESERIES ManagingEditor:ProfessorM.Reid,MathematicsInstitute, UniversityofWarwick,CoventryCV47AL,UnitedKingdom Thetitlesbelowareavailablefrombooksellers,orfromCambridgeUniversityPressat http://www.cambridge.org/mathematics 287 TopicsonRiemannsurfacesandFuchsiangroups,E.BUJALANCE,A.F.COSTA&E.MARTÍNEZ(eds) 288 Surveysincombinatorics,2001,J.W.P.HIRSCHFELD(ed) 289 AspectsofSobolev-typeinequalities,L.SALOFF-COSTE 290 QuantumgroupsandLietheory,A.PRESSLEY(ed) 291 Titsbuildingsandthemodeltheoryofgroups,K.TENT(ed) 292 Aquantumgroupsprimer,S.MAJID 293 SecondorderpartialdifferentialequationsinHilbertspaces,G.DAPRATO&J.ZABCZYK 294 Introductiontooperatorspacetheory,G.PISIER 295 Geometryandintegrability,L.MASON&Y.NUTKU(eds) 296 Lecturesoninvarianttheory,I.DOLGACHEV 297 Thehomotopycategoryofsimplyconnected4-manifolds,H.-J.BAUES 298 Higheroperads,highercategories,T.LEINSTER(ed) 299 Kleiniangroupsandhyperbolic3-manifolds,Y.KOMORI,V.MARKOVIC&C.SERIES(eds) 300 IntroductiontoMöbiusdifferentialgeometry,U.HERTRICH-JEROMIN 301 StablemodulesandtheD(2)-problem,F.E.A.JOHNSON 302 DiscreteandcontinuousnonlinearSchrödingersystems,M.J.ABLOWITZ,B.PRINARI&A.D.TRUBATCH 303 Numbertheoryandalgebraicgeometry,M.REID&A.SKOROBOGATOV(eds) 304 GroupsStAndrews2001inOxfordI,C.M.CAMPBELL,E.F.ROBERTSON&G.C.SMITH(eds) 305 GroupsStAndrews2001inOxfordII,C.M.CAMPBELL,E.F.ROBERTSON&G.C.SMITH(eds) 306 Geometricmechanicsandsymmetry,J.MONTALDI&T.RATIU(eds) 307 Surveysincombinatorics2003,C.D.WENSLEY(ed.) 308 Topology,geometryandquantumfieldtheory,U.L.TILLMANN(ed) 309 Coringsandcomodules,T.BRZEZINSKI&R.WISBAUER 310 Topicsindynamicsandergodictheory,S.BEZUGLYI&S.KOLYADA(eds) 311 Groups:topological,combinatorialandarithmeticaspects,T.W.MÜLLER(ed) 312 Foundationsofcomputationalmathematics,Minneapolis2002,F.CUCKERetal(eds) 313 Transcendentalaspectsofalgebraiccycles,S.MÜLLER-STACH&C.PETERS(eds) 314 Spectralgeneralizationsoflinegraphs,D.CVETKOVIC,P.ROWLINSON&S.SIMIC 315 Structuredringspectra,A.BAKER&B.RICHTER(eds) 316 Linearlogicincomputerscience,T.EHRHARD,P.RUET,J.-Y.GIRARD&P.SCOTT(eds) 317 Advancesinellipticcurvecryptography,I.F.BLAKE,G.SEROUSSI&N.P.SMART(eds) 318 Perturbationoftheboundaryinboundary-valueproblemsofpartialdifferentialequations,D.HENRY 319 DoubleaffineHeckealgebras,I.CHEREDNIK 320 L-functionsandGaloisrepresentations,D.BURNS,K.BUZZARD&J.NEKOVÁRˇ(eds) 321 Surveysinmodernmathematics,V.PRASOLOV&Y.ILYASHENKO(eds) 322 Recentperspectivesinrandommatrixtheoryandnumbertheory,F.MEZZADRI&N.C.SNAITH(eds) 323 Poissongeometry,deformationquantisationandgrouprepresentations,S.GUTTetal(eds) 324 Singularitiesandcomputeralgebra,C.LOSSEN&G.PFISTER(eds) 325 LecturesontheRicciflow,P.TOPPING 326 ModularrepresentationsoffinitegroupsofLietype,J.E.HUMPHREYS 327 Surveysincombinatorics2005,B.S.WEBB(ed) 328 Fundamentalsofhyperbolicmanifolds,R.CANARY,D.EPSTEIN&A.MARDEN(eds) 329 SpacesofKleiniangroups,Y.MINSKY,M.SAKUMA&C.SERIES(eds) 330 Noncommutativelocalizationinalgebraandtopology,A.RANICKI(ed) 331 Foundationsofcomputationalmathematics,Santander2005,L.MPARDO,A.PINKUS,E.SÜLI&M.J.TODD(eds) 332 Handbookoftiltingtheory,L.ANGELERIHÜGEL,D.HAPPEL&H.KRAUSE(eds) 333 Syntheticdifferentialgeometry(2ndEdition),A.KOCK 334 TheNavier–Stokesequations,N.RILEY&P.DRAZIN 335 Lecturesonthecombinatoricsoffreeprobability,A.NICA&R.SPEICHER 336 Integralclosureofideals,rings,andmodules,I.SWANSON&C.HUNEKE 337 MethodsinBanachspacetheory,J.M.F.CASTILLO&W.B.JOHNSON(eds) 338 Surveysingeometryandnumbertheory,N.YOUNG(ed) 339 GroupsStAndrews2005I,C.M.CAMPBELL,M.R.QUICK,E.F.ROBERTSON&G.C.SMITH(eds) 340 GroupsStAndrews2005II,C.M.CAMPBELL,M.R.QUICK,E.F.ROBERTSON&G.C.SMITH(eds) 341 Ranksofellipticcurvesandrandommatrixtheory,J.B.CONREY,D.W.FARMER,F.MEZZADRI&N.C.SNAITH(eds) 342 Ellipticcohomology,H.R.MILLER&D.C.RAVENEL(eds) 343 AlgebraiccyclesandmotivesI,J.NAGEL&C.PETERS(eds) 344 AlgebraiccyclesandmotivesII,J.NAGEL&C.PETERS(eds) 345 Algebraicandanalyticgeometry,A.NEEMAN 346 Surveysincombinatorics2007,A.HILTON&J.TALBOT(eds) 347 Surveysincontemporarymathematics,N.YOUNG&Y.CHOI(eds) 348 Transcendentaldynamicsandcomplexanalysis,P.J.RIPPON&G.M.STALLARD(eds) 349 ModeltheorywithapplicationstoalgebraandanalysisI,Z.CHATZIDAKIS,D.MACPHERSON,A.PILLAY& A.WILKIE(eds) 350 ModeltheorywithapplicationstoalgebraandanalysisII,Z.CHATZIDAKIS,D.MACPHERSON,A.PILLAY& A.WILKIE(eds) 351 FinitevonNeumannalgebrasandmasas,A.M.SINCLAIR&R.R.SMITH 352 Numbertheoryandpolynomials,J.MCKEE&C.SMYTH(eds) 353 Trendsinstochasticanalysis,J.BLATH,P.MÖRTERS&M.SCHEUTZOW(eds) 354 Groupsandanalysis,K.TENT(ed) 355 Non-equilibriumstatisticalmechanicsandturbulence,J.CARDY,G.FALKOVICH&K.GAWEDZKI 356 EllipticcurvesandbigGaloisrepresentations,D.DELBOURGO 357 Algebraictheoryofdifferentialequations,M.A.H.MACCALLUM&A.V.MIKHAILOV(eds) 358 Geometricandcohomologicalmethodsingrouptheory,M.R.BRIDSON,P.H.KROPHOLLER&I.J.LEARY(eds) 359 Modulispacesandvectorbundles,L.BRAMBILA-PAZ,S.B.BRADLOW,O.GARCÍA-PRADA&S.RAMANAN(eds) 360 Zariskigeometries,B.ZILBER 361 Words:Notesonverbalwidthingroups,D.SEGAL 362 Differentialtensoralgebrasandtheirmodulecategories,R.BAUTISTA,L.SALMERÓN&R.ZUAZUA 363 Foundationsofcomputationalmathematics,HongKong2008,F.CUCKER,A.PINKUS&M.J.TODD(eds) 364 Partialdifferentialequationsandfluidmechanics,J.C.ROBINSON&J.L.RODRIGO(eds) 365 Surveysincombinatorics2009,S.HUCZYNSKA,J.D.MITCHELL&C.M.RONEY-DOUGAL(eds) 366 Highlyoscillatoryproblems,B.ENGQUIST,A.FOKAS,E.HAIRER&A.ISERLES(eds) 367 Randommatrices:Highdimensionalphenomena,G.BLOWER 368 GeometryofRiemannsurfaces,F.P.GARDINER,G.GONZÁLEZ-DIEZ&C.KOUROUNIOTIS(eds) 369 Epidemicsandrumoursincomplexnetworks,M.DRAIEF&L.MASSOULIÉ 370 Theoryofp-adicdistributions,S.ALBEVERIO,A.YU.KHRENNIKOV&V.M.SHELKOVICH 371 Conformalfractals,F.PRZYTYCKI&M.URBAN´SKI 372 Moonshine:Thefirstquartercenturyandbeyond,J.LEPOWSKY,J.MCKAY&M.P.TUITE(eds) 373 Smoothness,regularityandcompleteintersection,J.MAJADAS&A.G.RODICIO 374 Geometricanalysisofhyperbolicdifferentialequations:Anintroduction,S.ALINHAC 375 Triangulatedcategories,T.HOLM,P.JØRGENSEN&R.ROUQUIER(eds) 376 Permutationpatterns,S.LINTON,N.RUŠKUC&V.VATTER(eds) 377 AnintroductiontoGaloiscohomologyanditsapplications,G.BERHUY 378 Probabilityandmathematicalgenetics,N.H.BINGHAM&C.M.GOLDIE(eds) 379 Finiteandalgorithmicmodeltheory,J.ESPARZA,C.MICHAUX&C.STEINHORN(eds) 380 Realandcomplexsingularities,M.MANOEL,M.C.ROMEROFUSTER&C.T.CWALL(eds) 381 Symmetriesandintegrabilityofdifferenceequations,D.LEVI,P.OLVER,Z.THOMOVA&P.WINTERNITZ(eds) 382 Forcingwithrandomvariablesandproofcomplexity,J.KRAJÍCˇEK 383 Motivicintegrationanditsinteractionswithmodeltheoryandnon-ArchimedeangeometryI,R.CLUCKERS, J.NICAISE&J.SEBAG(eds) 384 Motivicintegrationanditsinteractionswithmodeltheoryandnon-ArchimedeangeometryII,R.CLUCKERS, J.NICAISE&J.SEBAG(eds) 385 EntropyofhiddenMarkovprocessesandconnectionstodynamicalsystems,B.MARCUS,K.PETERSEN& T.WEISSMAN(eds) 386 Independence-friendlylogic,A.L.MANN,G.SANDU&M.SEVENSTER 387 GroupsStAndrews2009inBathI,C.M.CAMPBELLetal(eds) 388 GroupsStAndrews2009inBathII,C.M.CAMPBELLetal(eds) 389 Randomfieldsonthesphere,D.MARINUCCI&G.PECCATI 390 Localizationinperiodicpotentials,D.E.PELINOVSKY 391 Fusionsystemsinalgebraandtopology,M.ASCHBACHER,R.KESSAR&B.OLIVER 392 Surveysincombinatorics2011,R.CHAPMAN(ed) 393 Non-abelianfundamentalgroupsandIwasawatheory,J.COATESetal(eds) 394 Variationalproblemsindifferentialgeometry,R.BIELAWSKI,K.HOUSTON&M.SPEIGHT(eds) 395 Howgroupsgrow,A.MANN 396 Arithmeticdfferentialoperatorsoverthep-adicIntegers,C.C.RALPH&S.R.SIMANCA 397 Hyperbolicgeometryandapplicationsinquantumchaosandcosmology,J.BOLTE&F.STEINER(eds) 398 Mathematicalmodelsincontactmechanics,M.SOFONEA&A.MATEI 399 Circuitdoublecoverofgraphs,C.-Q.ZHANG 400 Densespherepackings:ablueprintforformalproofs,T.HALES 401 AdoubleHallalgebraapproachtoaffinequantumSchur-Weyltheory,B.DENG,J.DU&Q.FU 402 Mathematicalaspectsoffluidmechanics,J.ROBINSON,J.L.RODRIGO&W.SADOWSKI(eds) 403 Foundationsofcomputationalmathematics:Budapest2011,F.CUCKER,T.KRICK,A.SZANTO&A.PINKUS(eds) 404 Operatormethodsforboundaryvalueproblems,S.HASSI,H.S.V.DESNOO&F.H.SZAFRANIEC(eds) 405 Torsors,étalehomotopyandapplicationstorationalpoints,A.N.SKOROBOGATOV(ed) 406 Appalachiansettheory,J.CUMMINGS&E.SCHIMMERLING(eds) 407 Themaximalsubgroupsofthelow-dimensionalfiniteclassicalgroups,J.N.BRAY,D.F.HOLT&C.M.RONEY-DOUGAL 408 Complexityscience:theWarwickmaster’scourse,R.BALL,R.S.MACKAY&V.KOLOKOLTSOV(eds) 409 Surveysincombinatorics2013,S.BLACKBURN,S.GERKE&M.WILDON(eds) 410 Representationtheoryandharmonicanalysisofwreathproductsoffinitegroups,T.CECCHERINISILBERSTEIN, F.SCARABOTTI&F.TOLLI 411 Modulispaces,L.BRAMBILA-PAZ,O.GARCIA-PRADA,P.NEWSTEAD&R.THOMAS(eds) 412 Automorphismsandequivalencerelationsintopologicaldynamics,D.B.ELLIS&R.ELLIS 413 Optimaltransportation:theoryandapplications,Y.OLLIVIER,H.PAJOT&C.VILLANI(eds) LondonMathematicalSocietyLectureNoteSeries:414 Automorphic Forms and Galois Representations Volume 1 Editedby FRED DIAMOND King’sCollegeLondon PAYMAN L. KASSAEI McGillUniversity,Montréal MINHYONG KIM UniversityofOxford UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781107691926 (cid:2)c CambridgeUniversityPress2014 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2014 PrintedintheUnitedKingdombyCPIGroupLtd,CroydonCR04YY AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationdata Automorphicformsandgaloisrepresentations/editedbyFredDiamond,King’sCollege London,PaymanL.Kassaei,McGillUniversity,Montréal,MinhyongKim,Universityof Oxford. volumes<1–2>cm.–(LondonMathematicalSocietylecturenoteseries;414,415) PaperspresentedattheLondonMathematicalSociety,andEPSRC(GreatBritain EngineeringandPhysicalSciencesResearchCouncil),SymposiumonGalois RepresentationsandAutomorphicForms,heldattheUniversityofDurhamfrom July18–28,2011. ISBN978-1-107-69192-6(v.1)–ISBN978-1-107-69363-0(v.2) 1. Automorphicforms–Congresses. 2. Automorphicfunctions–Congresses. 3. Forms (Mathematics)–Congresses. 4. Galoistheory–Congresses. I. Diamond,Fred,editorof compilation. II. Kassaei,PaymanL.,1973–editorofcompilation. III. Kim,Minhyong, editorofcompilation. IV. SymposiumonGaloisRepresentationsandAutomorphic Forms(2011:Durham,England) QA353.A9A925 2014 515(cid:3).9–dc23 2014001841 ISBN978-1-107-69192-6Paperback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication, anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. Contents Listofcontributors pagevi Preface ix 1 Asemi-stablecaseoftheShafarevichConjecture 1 VictorAbrashkin 2 IrreduciblemodularrepresentationsoftheBorelsubgroupof GL (Q ) 32 2 p LaurentBergerandMathieuVienney 3 p-adic L-functionsandEulersystems:ataleintwotrilogies 52 MassimoBertolini,FrancescCastella,HenriDarmon,SamitDasgupta, KartikPrasanna,andVictorRotger 4 EffectivelocalLanglandscorrespondence 102 ColinJ.Bushnell 5 The conjectural connections between automorphic representationsandGaloisrepresentations 135 KevinBuzzardandTobyGee 6 Geometryofthefundamentallemma 188 Pierre-HenriChaudouard 7 The p-adicanalyticspaceofpseudocharactersofaprofinite groupandpseudorepresentationsoverarbitraryrings 221 GaëtanChenevier 8 LasérieprincipaleunitairedeGL (Q ):vecteurslocalement 2 p analytiques 286 PierreColmez 9 Equationsdifférentiellesp-adiquesetmodulesdeJacquet analytiques 359 GabrielDospinescu v Contributors Victor Abrashkin, Department of Mathematical Sciences, University of Durham,Durham,DH1,3LE,UK. Laurent Berger, UMPA, Ecole Normale Supérieure de Lyon, Lyon, 69007, France. Massimo Bertolini, Diparetimento di Matematica, Università di Milano, Milano20133,Italy. ColinBushnell,DepartmentofMathematics,King’sCollegeLondon,London, WC2R2LS,UK. Kevin Buzzard, Department of Mathematics, Imperial College London, London,SW72RH,UK. FrancescCastella,DepartmentofMathematics,UniversityofCalifornia,Los Angeles,CA90095-1555,USA. Pierre-Henri Chaudouard, Institut de Mathématiques de Jussieu, Université ParisDiderot(Paris7),75205ParisCedex13,France. Gaëtan Chenevier, Centre de Mathématiques Laurent Schwartz, École Poly- technique,Paris,91128PalaiseauCedex,France. Pierre Colmez, CNRS. Institute de Mathématiques de Jussieu, Paris, 75005, France. HenriDarmon,DepartmentofMathematicsandStatistics,McGillUniversity, Montreal,Canada,H3A0B9. SamitDasgupta,DepartmentofMathematics,UniveristyofCalifornia,Santa Cruz,CA95064,USA. vi Listofcontributors vii Gabriel Dospinescu, UMPA – UMR, Ecole Normale Supérieure de Lyon, 69 364LyonCedex07,France. Toby Gee, Department of Mathematics, Imperial College London, London, SW72RH,UK. Kartik Prasanna, Department of Mathematics, University of Michigan, Ann Arbor,MI48109-1043,USA. VictorRotger,MathemàticaAplicadaII,UniversitatPolitècnicadeCatalunya, Barcelona08034,Spain. Mathieu Vienney, UMPA, Ecole Normale Supérieure de Lyon, Lyon 69007, France.
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