On the Cohomology of Certain Non-Compact Shimura Varieties
Main description: 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...
שמור ב:
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| פורמט: | Livre numérique |
| שפה: | Anglais |
| יצא לאור: |
Princeton ; N.J :
Princeton University Press
2010.
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| סדרה: | Annals of Mathematics Studies
173 |
| נושאים: | |
| גישה מקוונת: | Accès Université d'Orléans et IFPM Accès INSA CVL |
| הערה: |
La pagination de l'édition imprimée correspondante est de : 232 p. Cyberlibris (ScholarVox) corpus Sciences de l'ingénieur Cyberlibris (ScholarVox) corpus Sciences de l'ingénieur |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • On the Cohomology of Certain Non-Compact Shimura Varieties, Texte imprimé, 9781400835393 |
| סיכום: | Main description: 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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| תאור פריט: | La pagination de l'édition imprimée correspondante est de : 232 p. Cyberlibris (ScholarVox) corpus Sciences de l'ingénieur Cyberlibris (ScholarVox) corpus Sciences de l'ingénieur |
| פורמט: | Nécessite un navigateur et un lecteur de fichier PDF |
| ISBN: | 9781400835393 |
| גישה: | L'accès complet à la ressource est réservé aux usagers des établissements qui en ont fait l'acquisition |