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On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173) (Annals of Mathematics Studies) - Couverture souple

Livre 25 sur 202: Annals of Mathematics Studies

Morel, Sophie

 
9780691142937: On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173) (Annals of Mathematics Studies)
Couverture souple
ISBN 10 : 0691142939 ISBN 13 : 9780691142937
Editeur : Princeton University Press, 2010

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

Sophie Morel is a member in the School of Mathematics at the Institute for Advanced Study in Princeton and a research fellow at the Clay Mathematics Institute.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Princeton University Press
Date d'édition
2010
Langue
anglais
ISBN 10 
0691142939
ISBN 13 
9780691142937
Reliure
Broché
Nombre de pages
230
Coordonnées du fabricant
non disponible
Personne responsable
Easy Access System Europe Oü, 16879218
gpsr.requests@easproject.com

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