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 タイトル: On the Galois actions on torsors of paths I, Descent of Galois representations 著者: Wojtkowiak, Zdzis{\l}aw キーワード: Galois groupfundamental grouptorsor of paths$\ell$-adic polylogarithmsLie algebraLie algebra of derivations 発行日: 2007年8月27日 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 14 (2007), No. 2, Page 177-259 抄録: We are studying representations obtained from actions of Galois groups on torsors of paths on a projective line minus a finite number of points. Using these actions on torsors of paths, we construct geometrically representations of Galois groups which realize $\ell$-adically the associated graded Lie algebra of the fundamental group of the tannakian category of mixed Tate motives over ${\rm Spec}\, \Zbb$, ${\rm Spec}\, \Zbb [i]$, ${\rm Spec}\, \Zbb [\frac{1}{q}]$, ${\rm Spec}\,\Oc _{\Qbb ( \sqrt {-q})}$ for any prime number $q$ ($q\neq 2$ in the last case) and over ${\rm Spec}\,\Oc _{\Qbb ( \sqrt {-q})}[\frac{1}{q}]$ for any prime number $q$ congruent to $3$ modulo $4$ and also for $q=2.$ URI: http://hdl.handle.net/2261/15754 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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