基础数论

图书标准信息

• 作者 [法]威尔 著
• 出版社 世界图书出版公司
• 出版时间 2010-01
• 版次 1
• ISBN 9787510004551
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 313页
• 正文语种 英语

【内容简介】

　　ThefirstpartofthisvolumeisbasedonacoursetaughtatPrinceton　Universityin1961-62;atthattime,anexcellentsetofnoteswasprepared　byDavidCantor,anditwasoriginallymyintentiontomakethesenotes　availabletothemathematicalpublicwithonlyquiteminorchanges.Then,amongsomeoldpapersofmine,Iaccidentallycameacrossalong-forgottenmanuscriptbyChevalley,ofpre-warvintage(forgotten,thatistosay,bothbymeandbyitsauthor)which,tomytasteatleast,seemedtohaveagedverywell.Itcontainedabriefbutessentiallycom-pleteaccountofthemainfeaturesofclassfieldtheory,bothlocalandglobal;anditsoonbecameobviousthattheusefulnessoftheintendedvolumewouldbegreatlyenhancedifIincludedsuchatreatmentofthistopic.Ithadtobeexpanded,inaccordancewithmyownplans,butitsoutlinecouldbepreservedwithoutmuchchange.Infact,Ihaveadheredtoitrathercloselyatsomecriticalpoints.

【作者简介】

Andre Weil 1906年5月6日出生于巴黎，1928年于巴黎大学获得博士学位，他曾先后在印度，法国，美国及巴西等国执教，1958年来到普林斯顿高等研究院从事研究工作，离休后现任该处终身教授。
Andre Weil的工作为抽象代数几何及Abel簇的现代理论的研究奠定了基础，他的大多数研究工作都在致力于建立“数论”、“代数几何”之间的联系，以及发明解析数论的现代方法。Weil是1934年左右成立的Ｂourbaki学派的创始人之一，此学派以集体名称N.Bourbaki出版了有着很高影响力的多卷专著《数学的基础》。

【目录】

Chronologicaltable
Prerequisitesandnotations
Tableofnotations

PARTⅠELEMENTARYTHEORY
ChapterⅠLocallycompactfields
1Finitefields
2Themoduleinalocallycompactfield
3Classificationoflocallycompactfields
4Structure0fp-fields

ChapterⅡLatticesanddualityoverlocalfields
1Norms
2Lattices
3Multiplicativestructureoflocalfields
4LatticesoverR
5Dualityoverlocalfields

ChapterⅢPlacesofA-fields
1A-fieldsandtheircompletions
2Tensor-productsofcommutativefields
3Tracesandnorms
4Tensor-productsofA-fieldsandlocalfields

ChapterⅣAdeles
1AdelesofA-fields
2Themaintheorems
3Ideles
4IdelesofA-fields

ChapterⅤAlgebraicnumber-fields
1，OrdersinalgebrasoverQ
2Latticesoveralgebraicnumber-fields
3Ideals
4Fundamentalsets

ChapterⅥThetheoremofRiemann-Roch
ChapterⅦZeta-functionsofA-fields
1ConvergenceofEulerproducts
2Fouriertransformsandstandardfunctions
3Quasicharacters
4QuasicharactersofA-fields
5Thefunctionalequation
6TheDedekindzeta-function
7L-functions
8ThecoefficientsoftheL-series

ChapterⅧTracesandnorms
1Tracesandnormsinlocalfields
2Calculationofthedifferent
3Ramificationtheory
4TracesandnormsinA-fields
5Splittingplacesinseparableextensions
6Anapplicationtoinseparableextensions

PARTⅡCLASSFIELDTHEORY
ChapterIXSimplealgebras
1Structureofsimplealgebras
2Therepresentationsofasimplealgebra
3Factor-setsandtheBrauergroup
4Cyclicfactor-sets
5Specialcyclicfactor-sets

ChapterⅩSimplealgebrasoverlocalfields
1Ordersandlattices
2Tracesandnorms
3Computationofsomeintegrals

ChapterⅪSimplealgebrasoverA-fields
1.Ramification
2.Thezeta-functionofasimplealgebra
3.Normsinsimplealgebras
4.Simplealgebrasoveralgebraicnumber-fields..

ChapterⅫ.Localclassfieldtheory
1.Theformalismofclassfieldtheory
2.TheBrauergroupofalocalfield
3.Thecanonicalmorphism
4.Ramificationofabelianextensions
5.Thetransfer

ChapterXIII.Globalclassfieldtheory
I.Thecanonicalpairing
2.Anelementarylemma
3.Hasses"lawofreciprocity".
4.ClassfieldtheoryforQ
5.TheHiibertsymbol
6.TheBrauergroupofanA-field
7.TheHilbertp-symbol
8.Thekernelofthecanonicalmorphism
9.Themaintheorems
10.Localbehaviorofabelianextensions
11."Classical"classfieldtheory
12."Coronidisloco".
Notestothetext
AppendixⅠ.Thetransfertheorem
AppendixⅡ.W-groupsforlocalfields
AppendixⅢ.Shafarevitchstheorem
AppendixⅣ.TheHerbranddistribution
Indexofdefinitions