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  1. Bog
  2. Geometri
  3. Algebraisk geometri

On the Cohomology of Certain Non-Compact Shimura Varieties

Af: Sophie Morel Engelsk Paperback

On the Cohomology of Certain Non-Compact Shimura Varieties

Af: Sophie Morel Engelsk Paperback
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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 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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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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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 232
ISBN-13: 9780691142937
Indbinding: Paperback
Udgave:
ISBN-10: 0691142939
Kategori: Algebraisk geometri
Udg. Dato: 24 jan 2010
Længde: 0mm
Bredde: 152mm
Højde: 235mm
Forlag: Princeton University Press
Oplagsdato: 24 jan 2010
Forfatter(e): Sophie Morel
Forfatter(e) Sophie Morel

Kategori Algebraisk geometri

ISBN-13 9780691142937

Sprog Engelsk

Indbinding Paperback

Sider 232

Udgave

Længde 0mm

Bredde 152mm

Højde 235mm

Udg. Dato 24 jan 2010

Oplagsdato 24 jan 2010

Forlag Princeton University Press

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