Difference between l-adic Galois representations and pro-l outer Galois representations associated to hyperbolic curves

作者：Iijima Yu^*

来源：Manuscripta Mathematica, 2017, 153(1-2): 129-145.

DOI：10.1007/s00229-016-0883-6

Let l be a prime number, and k a field of characteristic zero. In the present paper, we consider the issue of whether or not the image of the pro-l outer Galois representation associated to a hyperbolic curve over k is an l-adic Lie group. In particular, we prove that, if k satisfies a mild assumption concerning l, then the image of the pro-l outer Galois representation associated to a hyperbolic curve over k is not an l-adic Lie group. Also, we consider the issue of whether or not the image of the universal pro-l outer monodromy representation of the moduli stack of hyperbolic curves is an l-adic Lie group.

• 出版日期2017-5