Non-Fiction Books:

On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173)

Sorry, this product is not currently available to order

Here are some other products you might consider...

On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173)

Format

Hardback

Customer rating

Click to share your rating 0 ratings (0.0/5.0 average) Thanks for your vote!

Share this product

On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173) by Sophie Morel
Unavailable
Sorry, this product is not currently available to order

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.

Author Biography

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.
Release date Australia
February 16th, 2010
Author
Country of Publication
United States
Imprint
Princeton University Press
Pages
232
Dimensions
152x229x18
ISBN-13
9780691142920
Product ID
4003688

Customer reviews

Nobody has reviewed this product yet. You could be the first!

Write a Review

Marketplace listings

There are no Marketplace listings available for this product currently.
Already own it? Create a free listing and pay just 9% commission when it sells!

Sell Yours Here

Help & options

  • If you think we've made a mistake or omitted details, please send us your feedback. Send Feedback
  • If you have a question or problem with this product, visit our Help section. Get Help
Filed under...