论文标题
野生galois表示：一个具有较大惯性图像的高纤维曲线家族
Wild Galois representations: a family of hyperelliptic curves with large inertia image
论文作者
论文摘要
在这项工作中，我们将Arxiv：1812.05651的主要结果概括为高ellip曲曲线的家族，其潜在地减少了$ p $ - adic领域，该领域具有$ p $ $ p $，并且是$ \ ell $ $ \ ell $ ad的惯性图像，与与雅各布相关。我们将证明该GALOIS表示为未受到的字符的张量和有限群的不可还原表示，该量可以等于惯性图像（在这种情况下，易于确定表示表示）或$ C_2 $ extensension。在第二种情况下，有两个合适的表示形式，我们将明确描述Galois动作以确定正确的行动。
In this work we generalise the main result of arXiv:1812.05651 to the family of hyperelliptic curves with potentially good reduction over a $p$-adic field which have degree $p$ and the largest possible image of inertia under the $\ell$-adic Galois representation associated to its Jacobian. We will prove that this Galois representation factors as the tensor product of an unramified character and an irreducible representation of a finite group, which can be either equal to the inertia image (in which case the representation is easily determined) or a $C_2$-extension of it. In this second case, there are two suitable representations and we will describe the Galois action explicitly in order to determine the correct one.
