LEADER 05872nam 2201321Ia 450 001 9910778922503321 005 20200520144314.0 010 $a1-280-49465-4 010 $a9786613589880 010 $a1-4008-4273-5 024 7 $a10.1515/9781400842735 035 $a(CKB)2550000000097189 035 $a(EBL)878315 035 $a(OCoLC)854968413 035 $a(SSID)ssj0000652344 035 $a(PQKBManifestationID)11940308 035 $a(PQKBTitleCode)TC0000652344 035 $a(PQKBWorkID)10636908 035 $a(PQKB)11369482 035 $a(MiAaPQ)EBC878315 035 $a(StDuBDS)EDZ0000406949 035 $a(DE-B1597)447343 035 $a(OCoLC)979624184 035 $a(DE-B1597)9781400842735 035 $a(Au-PeEL)EBL878315 035 $a(CaPaEBR)ebr10546024 035 $a(CaONFJC)MIL358988 035 $z(PPN)199244995 035 $a(PPN)187959668 035 $a(EXLCZ)992550000000097189 100 $a20111011d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMumford-Tate groups and domains$b[electronic resource] $etheir geometry and arithmetic /$fMark Green, Phillip Griffiths, Matt Kerr 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$d2012 215 $a1 online resource (298 p.) 225 1 $aAnnals of mathematics studies ;$vno. 183 300 $aDescription based upon print version of record. 311 $a0-691-15424-4 311 $a0-691-15425-2 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tContents -- $tIntroduction -- $tChapter I. Mumford-Tate Groups -- $tChapter II. Period Domains and Mumford-Tate Domains -- $tChapter III. The Mumford-Tate Group of a Variation of Hodge Structure -- $tChapter IV. Hodge Representations and Hodge Domains -- $tChapter V. Hodge Structures With Complex Multiplication -- $tChapter VI. Arithmetic Aspects of Mumford-Tate Domains -- $tChapter VII. Classification of Mumford-Tate Subdomains -- $tChapter VIII. Arithmetic of Period Maps of Geometric Origin -- $tIndex 330 $aMumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on "ients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject. 410 0$aAnnals of mathematics studies ;$vno. 183. 606 $aMumford-Tate groups 606 $aGeometry, Algebraic 610 $aDeligne torus integer. 610 $aGalois group. 610 $aGrothendieck conjecture. 610 $aHodge decomposition. 610 $aHodge domain. 610 $aHodge filtration. 610 $aHodge orientation. 610 $aHodge representation. 610 $aHodge structure. 610 $aHodge tensor. 610 $aHodge theory. 610 $aKubota rank. 610 $aLie algebra representation. 610 $aLie group. 610 $aMumford-Tate domain. 610 $aMumford-Tate group. 610 $aMumford-Tate subdomain. 610 $aNoether-Lefschetz locus. 610 $aVogan diagram method. 610 $aWeyl group. 610 $aabelian variety. 610 $aabsolute Hodge class. 610 $aalgebraic geometry. 610 $aarithmetic group. 610 $aautomorphic cohomology. 610 $aclassical group. 610 $acompact dual. 610 $acomplex manifold. 610 $acomplex multiplication Hodge structure. 610 $acomplex multiplication. 610 $aendomorphism algebra. 610 $aexceptional group. 610 $aholomorphic mapping. 610 $ahomogeneous complex manifold. 610 $ahomomorphism. 610 $amixed Hodge structure. 610 $amoduli space. 610 $amonodromy group. 610 $anatural symmetry group. 610 $aoriented imaginary number fields. 610 $aperiod domain. 610 $aperiod map. 610 $apolarization. 610 $apolarized Hodge structure. 610 $apure Hodge structure. 610 $areflex field. 610 $asemisimple Lie algebra. 610 $asemisimple Lie group. 610 $a?-equivalence classes. 615 0$aMumford-Tate groups. 615 0$aGeometry, Algebraic. 676 $a516.35 686 $aSI 830$2rvk 700 $aGreen$b M$g(Mark)$0348041 701 $aGriffiths$b Phillip$f1938-$057421 701 $aKerr$b Matthew D.$f1975-$01506793 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910778922503321 996 $aMumford-Tate groups and domains$93737170 997 $aUNINA