A Motivic Grothendieck-Teichmüller群
A Motivic Grothendieck-Teichmüller Group
摘要：
本文证明了亏格为0的n个标志点曲线的模空间上的模的Beilinson-Soul{é}消失猜想.作为证明的一部分，也证明了这些动机是混杂的泰特。作为一个后果莱文的工作，然后得到定义良好的类别混合泰特动机的模空间的曲线。结果表明，模空间之间的态射遗忘标记点和嵌入作为边界组件诱导函子之间的这些类别和如何切基点适合在这些函子。Tannakian形式主义将群附加到这些范畴和态射上，反映了导致motivic Grothendieck-Teichm{ü}ller群定义的功能性。上述性质的证明依赖于模空间的塔的几何。这使我们能够处理Spec（Z）上动机的一般情况，其中积分系数在Spitzweck的动机类别中起作用。从那里，传递到Q系数，我们处理经典的tannakian形式主义，并解释如何在Spec（Q）上工作允许更具体地描述tannakian群。
英文摘要：
This paper proves the Beilinson-Soul{é} vanishing conjecture for motives attached to the moduli spaces of curves of genus 0 with n marked points. As part of the proof, it is also proved that these motives are mixed Tate. As a consequence of Levine's work, one obtains then well defined categories of mixed Tate motives over the moduli spaces of curves . It is shown that morphisms between moduli spaces forgetting marked points and embedding as boundary components induce functors between those categories and how tangential bases points fit in these functorialities. Tannakian formalism attaches groups to these categories and morphisms reflecting the functorialities leading to the definition of a motivic Grothendieck-Teichm{ü}ller group. Proofs of the above properties rely on the geometry of the tower of the moduli spaces . This allows us to treat the general case of motives over Spec(Z) with integral coefficients working in Spitzweck's category of motives. From there, passing to Q-coefficients we deal with the classical tannakian formalism and explain how working over Spec(Q) allows a more concrete description of the tannakian group.
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