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S1474748010000241.pdf | 207.19 kB | Adobe PDF | 見る/開く |
タイトル: | Braid monodromies on proper curves and pro-ℓ Galois representations |
著者: | Takao, Naotake |
著者名の別形: | 高尾, 尚武 |
キーワード: | proper hyperbolic curve braid group mapping class group Lie algebra pro-ℓ Galois representation universal monodromy representation |
発行日: | Jan-2012 |
出版者: | Cambridge University Press |
誌名: | Journal of the Institute of Mathematics of Jussieu |
巻: | 11 |
号: | 01 |
開始ページ: | 161 |
終了ページ: | 188 |
抄録: | Let C be a proper smooth geometrically connected hyperbolic curve over a field of characteristic 0 and ℓ a prime number. We prove the injectivity of the homomorphism from the pro-ℓ mapping class group attached to the two dimensional configuration space of C to the one attached to C, induced by the natural projection. We also prove a certain graded Lie algebra version of this injectivity. Consequently, we show that the kernel of the outer Galois representation on the pro-ℓ pure braid group on C with n strings does not depend on n, even if n = 1. This extends a previous result by Ihara–Kaneko. By applying these results to the universal family over the moduli space of curves, we solve completely Oda's problem on the independency of certain towers of (infinite) algebraic number fields, which has been studied by Ihara, Matsumoto, Nakamura, Ueno and the author. Sequentially we obtain certain information of the image of this Galois representation and get obstructions to the surjectivity of the Johnson–Morita homomorphism at each sufficiently large even degree (as Oda predicts), for the first time for a proper curve. |
著作権等: | © Cambridge University Press 2012 This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。 |
URI: | http://hdl.handle.net/2433/152367 |
DOI(出版社版): | 10.1017/S1474748010000241 |
出現コレクション: | 学術雑誌掲載論文等 |
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