Franklin

On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173) / Sophie Morel.

Author/Creator:
Morel, Sophie author.
Publication:
Princeton, NJ : Princeton University Press, [2010]
Format/Description:
Book
1 online resource
Edition:
Course Book
Series:
Annals of Mathematics Studies ; 194
Contained In:
De Gruyter University Press Library.
Status/Location:
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Details

Subjects:
Homology theory.
Shimura varieties.
Language:
In English.
System Details:
Mode of access: Internet via World Wide Web.
text file PDF
Summary:
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.
Contents:
Frontmatter
Contents
Preface
Chapter 1. The fixed point formula
Chapter 2. The groups
Chapter 3. Discrete series
Chapter 4. Orbital integrals at p
Chapter 5. The geometric side of the stable trace formula
Chapter 6. Stabilization of the fixed point formula
Chapter 7. Applications
Chapter 8. The twisted trace formula
Chapter 9. The twisted fundamental lemma
Appendix. Comparison of two versions of twisted transfer factors
Bibliography
Index
Notes:
Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)
Contributor:
De Gruyter.
ISBN:
9781400835393
OCLC:
979579419
Publisher Number:
10.1515/9781400835393 doi
Access Restriction:
Restricted for use by site license.