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1、LectureNotesinMathematicsAcollectionofinformalreportsandseminarsEditedbyA.Dold,HeidelbergandB.Eckmann,Z0rich203DonaldKnutsonColumbiaUniversityintheCityofNewYork,NewYork,NY/USAAlgebraicSpacesSpringer-VerlagBerlin.Heidelberg-NewYork1971AMSSubjectClassifications(1970):14-02,14A15,14A20,14F20,18F10ISB
2、N3-540-05496-0Springer-VerlagBerlinHeidelberg-NewYorkISBN0-387-05496-0Springer-VerlagNewYorkHeidelbergBerlinThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallythoseoftranslation,reprinting,re-useofillustrations,broadcasting,reproductionbypho
3、tocopyingmachineorsimilarmeans,andstorageindatabanks.Under§54oftheGermanCopyrightLawwherecopiesaremadeforotherthanprivateuse,afeeispayabletothepublisher,theamountofthefeetobedeterminedbyagreemzntwiththepublisher.©bySpringer-VerlagBerlin.Heidelberg1971.LibraryofCongressCatalogCardNumber73-164957.Pr
4、intedinGermany.Offsetdruck:JuliusBeltz,HemsbachPREPACEThecoreofthisbookistheauthor'sthesis,AlgebraicSpaces,writtenunderMichaelArtinatthe~assachusettsInstituteofTechnology.TheobjectthereasherewastoworkoutthefoundationslaEGAforthetheoryofalgebraicspaces,andhencegivethenecessarybackgroundforArtin'sfu
5、ndamentalpapersAl~ebraizationofFormalModuliI,II.Whileworkingonthisbook,IwassupportedbyM.I.T.,BostonCollege,ColumbiaUniversity,andtheAdvancedScienceSummerSeminaratBowdoinCollege,sponsoredbytheNationalScienceFoundation.Toalltheseinstitutions,Iextendmygratitude.MyspecialthanksgoestoProfessorMichaelAr
6、tinbothformanyhelpfuldiscussionsandforhisinitialsuggestionthatIundertakethisproject.DonaldKnutsonCONTENTSIntroduction..........................IChapterOne:TheEtaleTopologyofSchemes...........29I.GrothendieckTopologiesandDescentTheory.......292.TheZariskiTopologyofSchemes.............383.TheFlatTop
7、ologyofSchemes..............524.TheEtaleTopologyofSchemes..............595.EtaleEquivalenceRelations...............72ChapterTwo:AlgebraicSpaces.................91I.TheCategoryofAlgebraicSpaces............912.TheE
