Mendeley出力
＜図書＞
The geometry and cohomology of some simple Shimura varieties
| 責任表示 | by Michael Harris and Richard Taylor ; with an appendix by Vladimir G. Berkovich |
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| シリーズ | Annals of mathematics studies ; no. 151 |
| データ種別 | 図書 |
| 出版情報 | Princeton, N.J. : Princeton University Press , 2001 |
| 本文言語 | 英語 |
| 大きさ | viii, 276 p. ; 24 cm |
| 概要 | This book aims first to prove the local Langlands conjecture for GL n over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic coho...ology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GL n (K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GL n (K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary. Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory. This book aims first to prove the local Langlands conjecture for GL n over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GL n (K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GL n (K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary. Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory. 続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6970948 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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: cloth | 理系図3F 数理独自 | HARR/42/1 | 2001 |
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023212001006472 |
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書誌詳細
| 一般注記 | Bibliography: p. 261-267 Includes index |
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| 著者標目 | *Harris, Michael Taylor, Richard Berkovich, Vladimir G. |
| 件 名 | LCSH:Shimura varieties LCSH:Cohomology operations |
| 分 類 | DC21:512.7 |
| 書誌ID | 1001387242 |
| ISBN | 0691090904 |
| NCID | BA54064022 |
| 巻冊次 | : cloth ; ISBN:0691090904 : pbk ; ISBN:0691090920 |
| 登録日 | 2009.11.02 |
| 更新日 | 2009.11.02 |