On the Galois actions on torsors of paths I, Descent of Galois representations

Journal of Mathematical Sciences

Wojtkowiak, Zdzis{l}aw¹ 

关键词: Galois group;    fundamental group;    torsor of paths;    $ell$-adic polylogarithms;    Lie algebra;    Lie algebra of derivations;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

WearestudyingrepresentationsobtainedfromactionsofGaloisgroupsontorsorsofpathsonaprojectivelineminusafinitenumberofpoints.Usingtheseactionsontorsorsofpaths,weconstructgeometricallyrepresentationsofGaloisgroupswhichrealize$ell$-adicallytheassociatedgradedLiealgebraofthefundamentalgroupofthetannakiancategoryofmixedTatemotivesover${mSpec},bb$,${mSpec},bb[i]$,${mSpec},bb[frac{1}{q}]$,${mSpec},Oc_{Qbb(sqrt{-q})}$foranyprimenumber$q$($qeq2$inthelastcase)andover${mSpec},Oc_{Qbb(sqrt{-q})}[frac{1}{q}]$foranyprimenumber$q$congruentto$3$modulo$4$andalsofor$q=2.$

【 授权许可】

Unknown