LEADER 04367nam 2200661Ia 450 001 9910465100703321 005 20200520144314.0 010 $a1-299-33300-1 010 $a1-4008-4601-3 024 7 $a10.1515/9781400846016 035 $a(CKB)2560000000100780 035 $a(EBL)1105284 035 $a(OCoLC)832314069 035 $a(SSID)ssj0000854075 035 $a(PQKBManifestationID)12383914 035 $a(PQKBTitleCode)TC0000854075 035 $a(PQKBWorkID)10902196 035 $a(PQKB)11704164 035 $a(MiAaPQ)EBC1105284 035 $a(StDuBDS)EDZ0001059463 035 $a(DE-B1597)448023 035 $a(OCoLC)979624321 035 $a(DE-B1597)9781400846016 035 $a(Au-PeEL)EBL1105284 035 $a(CaPaEBR)ebr10674438 035 $a(CaONFJC)MIL464550 035 $a(EXLCZ)992560000000100780 100 $a20120723d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aArithmetic compactifications of PEL-type Shimura varieties$b[electronic resource] /$fKai-Wen Lan 205 $aCourse Book 210 $aPrinceton, NJ $cPrinceton University Press$d2013 215 $a1 online resource (588 p.) 225 1 $aLondon Mathematical Society monographs ;$vVol. 36 300 $aDescription based upon print version of record. 311 $a0-691-15654-9 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tContents -- $tAcknowledgments -- $tIntroduction -- $tChapter One. Definition of Moduli Problems -- $tChapter Two. Representability of Moduli Problems -- $tChapter Three. Structures of Semi-Abelian Schemes -- $tChapter Four. Theory of Degeneration for Polarized Abelian Schemes -- $tChapter Five. Degeneration Data for Additional Structures -- $tChapter Six. Algebraic Constructions of Toroidal Compactifications -- $tChapter Seven. Algebraic Constructions of Minimal Compactifications -- $tAppendix A. Algebraic Spaces and Algebraic Stacks -- $tAppendix B. Deformations and Artin's Criterion -- $tBibliography -- $tIndex 330 $aBy studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. The book is designed to be accessible to graduate students who have an understanding of schemes and abelian varieties. PEL-type Shimura varieties, which are natural generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have played important roles in the development of the Langlands program. As with modular curves, it is desirable to have integral models of compactifications of PEL-type Shimura varieties that can be described in sufficient detail near the boundary. This book explains in detail the following topics about PEL-type Shimura varieties and their compactifications: A construction of smooth integral models of PEL-type Shimura varieties by defining and representing moduli problems of abelian schemes with PEL structures An analysis of the degeneration of abelian varieties with PEL structures into semiabelian schemes, over noetherian normal complete adic base rings A construction of toroidal and minimal compactifications of smooth integral models of PEL-type Shimura varieties, with detailed descriptions of their structure near the boundary Through these topics, the book generalizes the theory of degenerations of polarized abelian varieties and the application of that theory to the construction of toroidal and minimal compactifications of Siegel moduli schemes over the integers (as developed by Mumford, Faltings, and Chai). 410 0$aLondon Mathematical Society monographs ;$vnew ser., no. 36. 606 $aShimura varieties 606 $aArithmetical algebraic geometry 608 $aElectronic books. 615 0$aShimura varieties. 615 0$aArithmetical algebraic geometry. 676 $a516.3/5 700 $aLan$b Kai-Wen$0521644 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465100703321 996 $aArithmetic compactifications of PEL-type Shimura varieties$9837107 997 $aUNINA