Abstract/Details

Weight spectral sequence and Hecke correspondence on Shimura varieties


2006 2006

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Abstract (summary)

The purpose of this paper is twofold. First, we elaborate the construction of T. Saito on the action of algebraic correspondence on the l-adic cohomology of varieties over local fields with semistable reduction and derive a recursive formula to compute the actions on the weight spectral sequence. Secondly, applying this to a certain kind of unitary Shimura varieties, we elaborate and complement the work of R. Taylor and the author on the compatibility of local and global Langlands correspondences. More specifically, we explicitly compute the action of (affine) Iwahori-Hecke algebra of GLn over p-adic field on the weight spectral sequence for unitary Shimura varieties with Iwahori level structure. This enables a full representation-theoretic elaboration of the results in the previous work, in particular the key vanishing result on the cohomology of Igusa varieties, and reproves the local-global compatibility somewhat more directly. Also, the local nature of the computation of the Hecke correspondence is interesting in its own right---it is an analogue of the classical Eichler-Shimura congruence relation, which amounts to finding some part of the cohomology of the Shimura variety by directly computing the action of Hecke correspondences on vanishing cycle sheaves.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Algebraic number theory; Hecke correspondence; Shimura varieties; Weight spectral sequence
Title
Weight spectral sequence and Hecke correspondence on Shimura varieties
Author
Yoshida, Teruyoshi
Number of pages
58
Publication year
2006
Degree date
2006
School code
0084
Source
DAI-B 67/05, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780542694684
Advisor
Taylor, Richard
University/institution
Harvard University
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3217943
ProQuest document ID
305344428
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305344428
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