LEADER 03739nam 22005895 450 001 9910465208903321 005 20210114075530.0 010 $a1-4008-3720-0 024 7 $a10.1515/9781400837205 035 $a(CKB)2560000000080605 035 $a(EBL)1744818 035 $a(OCoLC)884646577 035 $a(DE-B1597)446204 035 $a(OCoLC)1013938914 035 $a(OCoLC)979954342 035 $a(DE-B1597)9781400837205 035 $a(MiAaPQ)EBC1744818 035 $a(EXLCZ)992560000000080605 100 $a20190708d2001 fg 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151), Volume 151 /$fRichard Taylor, Michael Harris 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2001] 210 4$dİ2002 215 $a1 online resource (288 p.) 225 0 $aAnnals of Mathematics Studies ;$v163 300 $aDescription based upon print version of record. 311 $a0-691-09092-0 327 $tFrontmatter -- $tContents -- $tIntroduction -- $tAcknowledgements -- $tChapter I. Preliminaries -- $tChapter II. Barsotti-Tate groups -- $tChapter III. Some simple Shimura varieties -- $tChapter IV. Igusa varieties -- $tChapter V. Counting Points -- $tChapter VI. Automorphic forms -- $tChapter VII. Applications -- $tAppendix. A result on vanishing cycles / $rBerkovich, V. G. -- $tBibliography -- $tIndex 330 $aThis book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GLn(K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GLn(K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary. Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory. 410 0$aAnnals of Mathematics Studies 606 $aMathematics$vGeometry$vGeneral 606 $aMathematics$vNumber Theory 606 $aShimura varieties 606 $aMATHEMATICS / Number Theory$2bisacsh 608 $aElectronic books. 615 0$aMathematics 615 0$aMathematics 615 0$aShimura varieties. 615 7$aMATHEMATICS / Number Theory. 676 $a516.3/5 700 $aHarris$b Michael, $066777 702 $aTaylor$b Richard, 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910465208903321 996 $aThe Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151), Volume 151$92491227 997 $aUNINA