LEADER 06009nam  2201441Ia 450 
001 9910780861803321
005 20200520144314.0
010   $a1-282-45800-0
010   $a1-282-93632-8
010   $a9786612936326
010   $a9786612458002
010   $a1-4008-3539-9
024 7 $a10.1515/9781400835393
035   $a(CKB)2520000000007008
035   $a(EBL)483574
035   $a(OCoLC)697182451
035   $a(SSID)ssj0000398714
035   $a(PQKBManifestationID)11955110
035   $a(PQKBTitleCode)TC0000398714
035   $a(PQKBWorkID)10363143
035   $a(PQKB)11773722
035   $a(MiAaPQ)EBC483574
035   $a(DE-B1597)446909
035   $a(OCoLC)979579419
035   $a(DE-B1597)9781400835393
035   $a(MiAaPQ)EBC4968598
035   $a(Au-PeEL)EBL483574
035   $a(CaPaEBR)ebr10364754
035   $a(CaONFJC)MIL293632
035   $a(Au-PeEL)EBL4968598
035   $a(CaONFJC)MIL245800
035   $a(OCoLC)741250592
035   $z(PPN)199244561
035   $a(PPN)187955492
035   $a(EXLCZ)992520000000007008
100   $a20090901d2010      uy             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aOn the cohomology of certain noncompact Shimura varieties$b[electronic resource] /$fSophie Morel; with an appendix by Robert Kottwitz
205   $aCourse Book
210   $aPrinceton $cPrinceton University Press$dc2010
215   $a1 online resource (231 p.)
225 0 $aAnnals of mathematics ;$v173
300   $aDescription based upon print version of record.
311   $a0-691-14292-0 
311   $a0-691-14293-9 
320   $aIncludes bibliographical references and index.
327   $t Frontmatter -- $tContents -- $tPreface -- $tChapter 1. The fixed point formula -- $tChapter 2. The groups -- $tChapter 3. Discrete series -- $tChapter 4. Orbital integrals at p -- $tChapter 5. The geometric side of the stable trace formula -- $tChapter 6. Stabilization of the fixed point formula -- $tChapter 7. Applications -- $tChapter 8. The twisted trace formula -- $tChapter 9. The twisted fundamental lemma -- $tAppendix. Comparison of two versions of twisted transfer factors -- $tBibliography -- $tIndex
330   $aThis book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. In general, these varieties are not compact. The intersection cohomology of the Shimura variety associated to a reductive group G carries commuting actions of the absolute Galois group of the reflex field and of the group G(Af) of finite adelic points of G. The second action can be studied on the set of complex points of the Shimura variety. In this book, Sophie Morel identifies the Galois action--at good places--on the G(Af)-isotypical components of the cohomology. Morel uses the method developed by Langlands, Ihara, and Kottwitz, which is to compare the Grothendieck-Lefschetz fixed point formula and the Arthur-Selberg trace formula. The first problem, that of applying the fixed point formula to the intersection cohomology, is geometric in nature and is the object of the first chapter, which builds on Morel's previous work. She then turns to the group-theoretical problem of comparing these results with the trace formula, when G is a unitary group over Q. Applications are then given. In particular, the Galois representation on a G(Af)-isotypical component of the cohomology is identified at almost all places, modulo a non-explicit multiplicity. Morel also gives some results on base change from unitary groups to general linear groups.
410  0$aAnnals of Mathematics Studies
606   $aShimura varieties
606   $aHomology theory
610   $aAccuracy and precision.
610   $aAdjoint.
610   $aAlgebraic closure.
610   $aArchimedean property.
610   $aAutomorphism.
610   $aBase change map.
610   $aBase change.
610   $aCalculation.
610   $aClay Mathematics Institute.
610   $aCoefficient.
610   $aCompact element.
610   $aCompact space.
610   $aComparison theorem.
610   $aConjecture.
610   $aConnected space.
610   $aConnectedness.
610   $aConstant term.
610   $aCorollary.
610   $aDuality (mathematics).
610   $aExistential quantification.
610   $aExterior algebra.
610   $aFinite field.
610   $aFinite set.
610   $aFundamental lemma (Langlands program).
610   $aGalois group.
610   $aGeneral linear group.
610   $aHaar measure.
610   $aHecke algebra.
610   $aHomomorphism.
610   $aL-function.
610   $aLogarithm.
610   $aMathematical induction.
610   $aMathematician.
610   $aMaximal compact subgroup.
610   $aMaximal ideal.
610   $aMorphism.
610   $aNeighbourhood (mathematics).
610   $aOpen set.
610   $aParabolic induction.
610   $aPermutation.
610   $aPrime number.
610   $aRamanujan?Petersson conjecture.
610   $aReductive group.
610   $aRing (mathematics).
610   $aScientific notation.
610   $aShimura variety.
610   $aSimply connected space.
610   $aSpecial case.
610   $aSub"ient.
610   $aSubalgebra.
610   $aSubgroup.
610   $aSymplectic group.
610   $aTheorem.
610   $aTrace formula.
610   $aUnitary group.
610   $aWeyl group.
615  0$aShimura varieties.
615  0$aHomology theory.
676   $a516.3/52
686   $aSI 830$2rvk
700   $aMorel$b Sophie$f1979-$01505634
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910780861803321
996   $aOn the cohomology of certain noncompact Shimura varieties$93735313
997   $aUNINA