LEADER 02993nam 22006015 450 001 9910146284103321 005 20250801064911.0 010 $a3-540-49728-5 024 7 $a10.1007/BFb0093051 035 $a(CKB)1000000000437363 035 $a(SSID)ssj0000326119 035 $a(PQKBManifestationID)12049806 035 $a(PQKBTitleCode)TC0000326119 035 $a(PQKBWorkID)10264787 035 $a(PQKB)11466165 035 $a(DE-He213)978-3-540-49728-8 035 $a(MiAaPQ)EBC5592078 035 $a(Au-PeEL)EBL5592078 035 $a(OCoLC)1066188859 035 $a(MiAaPQ)EBC6842322 035 $a(Au-PeEL)EBL6842322 035 $a(OCoLC)159930201 035 $a(PPN)155227513 035 $a(EXLCZ)991000000000437363 100 $a20121227d1997 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aRealizations of Polylogarithms /$fby Jörg Wildeshaus 205 $a1st ed. 1997. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1997. 215 $a1 online resource (XII, 344 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1650 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-62460-0 327 $aMixed structures on fundamental groups -- The canonical construction of mixed sheaves on mixed shimura varieties -- Polylogarithmic extensions on mixed shimura varieties. Part I: Construction and basic properties -- Polylogarithmic extensions on mixed shimura varieties. part II: The classifical polylogarithm -- Polygogarithmic extensions on mixed shimura varieties. Part III: The elliptic polygogarithm. 330 $aClassically, higher logarithms appear as multivalued functions on the projective line. Today they can be interpreted as entries of the period matrix of a certain variation of Hodge structure, itself called the "polylogarithm". The aim of the book is to document the sheaf-theoretical foundations of the field of polylogarithms. Earlier, partly unpublished results and constructions of Beilinson, Deligne, and Levin on the classical and elliptic polylog are generalized to the context of Shimura varieties. The reader is expected to have a sound background in algebraic geometry. Large parts of the book are expository, and intended as a reference for the working mathematician. Where a self-contained exposition was not possible, the author gives references in order to make the material accessible for advanced graduate students. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v1650 606 $aNumber theory 606 $aNumber Theory 615 0$aNumber theory. 615 14$aNumber Theory. 676 $a512.7 700 $aWildeshaus$b Jo?rg$f1965-$0351016 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146284103321 996 $aRealizations of polylogarithms$978836 997 $aUNINA