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Sophie Morel, "On the Cohomology of Certain Non-Compact Shimura Varieties"

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.

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	Science/Engineering Automorphic Forms, Shimura Varieties and L-Functions, Volume 2 Laurent Clozel, “Automorphic Forms, Shimura Varieties and L-Functions, Volume 2” Academic Pr \| 1990-01 \| ISBN: 0121766527 \| 408 pages \| PDF \| 12,6 MB Automorphic Forms, Shimura Varieties and L-Functions: Proceedings of a Conference Held ...
	Science/Engineering Automorphic Forms, Shimura Varieties and L-Functions Laurent Clozel, “Automorphic Forms, Shimura Varieties and L-Functions” Academic Pr \| 1990-01 \| ISBN: 0121766519 \| 456 pages \| PDF \| 20,4 MB Automorphic Forms, Shimura Varieties and L-Functions: Proceedings of a Conference Held at the Un ...
	Science/Engineering Continuous Bounded Cohomology of Locally Compact Groups Continuous Bounded Cohomology of Locally Compact GroupsPublisher: Springer \| Pages: 214 \| 2001-06-27 \| ISBN 3540420541 \| DJVU \| 2 MBRecent research has repeatedly led to connections between important rigidity questions and bounded coh ...
	Science/Engineering Toroidal Groups : Line Bundles, Cohomology and Quasi-Abelian Varieties Toroidal Groups : Line Bundles, Cohomology and Quasi-Abelian VarietiesSpringer \| June 15, 2001 \| ISBN-10: 3540419896 \| 133 pages \| PDF \| 1.5 mbDiscusses line bundles, cohomology and quasiabelian varieties of toroidal groups. Softcover.pass ...
	Harmonic Analysis, the Trace Formula, and Shimura Varieties Harmonic Analysis, the Trace Formula, and Shimura Varieties Publisher: American Mathematical Society \| ISBN: 082183844X \| edition 2005 \| PDF \| 689 pages \| 4,33 mbThe modern theory of automorphic forms, embodied in what has come to be known ...
	Technical Automorphic Forms and Shimura Varieties of PGSp(2) Automorphic Forms and Shimura Varieties of PGSp(2)Publisher: World Scientific Publishing Company \| ISBN: 9812564039 \| edition 2005 \| PDF \| 324 pages \| 4,09 mbThe area of automorphic representations is a natural continuation of studies in th ...

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