On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173) /

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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 g...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Morel, Sophie (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2010]
Edición:Course Book
Colección:Annals of Mathematics Studies ; 173
Temas:
Homology theory.
Shimura varieties.
MATHEMATICS / Topology.
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.
Acceso en línea:Texto completo
Texto completo
Descripción
Sumario: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.
Descripción Física:1 online resource (232 p.)
ISBN:9781400835393
9783110494914
9783110442502
Acceso:restricted access

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