| 翻訳と辞書 |
| Local Langlands conjectures ： ウィキペディア英語版 |
Local Langlands conjectures
In mathematics, the local Langlands conjectures, introduced by , are part of the Langlands program. They describe a correspondence between the complex representations of a reductive algebraic group ''G'' over a local field ''F'', and representations of the Langlands group of ''F'' into the L-group of ''G''. This correspondence is not a bijection in general. The conjectures can be thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois groups.
==Local Langlands conjectures for GL1==
The local Langlands conjectures for GL1(''K'') follow from (and are essentially equivalent to) local class field theory. More precisely the Artin map gives an isomorphism from the group GL1(''K'')= ''K''
* to the abelianization of the Weil group. In particular irreducible smooth representations of GL1(''K'') are 1-dimensional as the group is abelian, so can be identified with homomorphisms of the Weil group to GL1(C). This gives the Langlands correspondence between homomorphisms of the Weil group to GL1(C) and
irreducible smooth representations of GL1(''K'').
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Local Langlands conjectures」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|