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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Book Description Condition: New. Buy with confidence! Book is in new, never-used condition. Seller Inventory # bk0691142939xvz189zvxnew
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Book Description PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # WP-9780691142937
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Book Description Condition: New. Studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. The author also 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. Series: Annals of Mathematics Studies. Num Pages: 232 pages, black & white illustrations, figures. BIC Classification: PBMW. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 229 x 152 x 15. Weight in Grams: 306. . 2010. Paperback. . . . . Seller Inventory # V9780691142937
Book Description paperback. Condition: New. Language: ENG. Seller Inventory # 9780691142937
Book Description Paperback / softback. Condition: New. New copy - Usually dispatched within 4 working days. Studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. The author also 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. Seller Inventory # B9780691142937
Book Description Condition: New. Seller Inventory # 6081298-n
Book Description Condition: New. New! This book is in the same immaculate condition as when it was published. Seller Inventory # 353-0691142939-new
Book Description PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # WP-9780691142937