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On the cohomology of certain noncompact Shimura varieties [[electronic resource] /] / Sophie Morel; with an appendix by Robert Kottwitz



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Autore: Morel Sophie <1979-> Visualizza persona
Titolo: On the cohomology of certain noncompact Shimura varieties [[electronic resource] /] / Sophie Morel; with an appendix by Robert Kottwitz Visualizza cluster
Pubblicazione: Princeton, : Princeton University Press, c2010
Edizione: Course Book
Descrizione fisica: 1 online resource (231 p.)
Disciplina: 516.3/52
Soggetto topico: Shimura varieties
Homology theory
Soggetto non controllato: Accuracy and precision
Adjoint
Algebraic closure
Archimedean property
Automorphism
Base change map
Base change
Calculation
Clay Mathematics Institute
Coefficient
Compact element
Compact space
Comparison theorem
Conjecture
Connected space
Connectedness
Constant term
Corollary
Duality (mathematics)
Existential quantification
Exterior algebra
Finite field
Finite set
Fundamental lemma (Langlands program)
Galois group
General linear group
Haar measure
Hecke algebra
Homomorphism
L-function
Logarithm
Mathematical induction
Mathematician
Maximal compact subgroup
Maximal ideal
Morphism
Neighbourhood (mathematics)
Open set
Parabolic induction
Permutation
Prime number
Ramanujan–Petersson conjecture
Reductive group
Ring (mathematics)
Scientific notation
Shimura variety
Simply connected space
Special case
Sub"ient
Subalgebra
Subgroup
Symplectic group
Theorem
Trace formula
Unitary group
Weyl group
Classificazione: SI 830
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Frontmatter -- Contents -- Preface -- Chapter 1. The fixed point formula -- Chapter 2. The groups -- Chapter 3. Discrete series -- Chapter 4. Orbital integrals at p -- Chapter 5. The geometric side of the stable trace formula -- Chapter 6. Stabilization of the fixed point formula -- Chapter 7. Applications -- Chapter 8. The twisted trace formula -- Chapter 9. The twisted fundamental lemma -- Appendix. Comparison of two versions of twisted transfer factors -- Bibliography -- Index
Sommario/riassunto: This 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.
Titolo autorizzato: On the cohomology of certain noncompact Shimura varieties  Visualizza cluster
ISBN: 1-282-45800-0
1-282-93632-8
9786612936326
9786612458002
1-4008-3539-9
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910780861803321
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Serie: Annals of Mathematics Studies