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.
General
Imprint: |
Princeton University Press
|
Country of origin: |
United States |
Series: |
Annals of Mathematics Studies |
Release date: |
February 2010 |
First published: |
2010 |
Authors: |
Sophie Morel
|
Dimensions: |
235 x 152 x 12mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
232 |
ISBN-13: |
978-0-691-14293-7 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
Algebraic geometry
|
LSN: |
0-691-14293-9 |
Barcode: |
9780691142937 |
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