论文标题
$ \ ell \ ell \ neq p $上升$ g $价态的galois表示
Lifting $G$-Valued Galois Representations when $\ell \neq p$
论文作者
论文摘要
在本文中，我们研究了当$ \ ell \ neq p $时，在任意还原组方案中价值的本地Galois表示的通用提升空间。特别是，在适用于任何根基准的某些技术条件下，我们在此类空间中构造了一个规范的平滑组件，从而推广了先前研究的经典组的最小化变形条件。我们的方法涉及将同型分解的概念扩展为$ \ textrm {gl} _n $ valued表示形式，向一般还原组方案。为了处理来自这个概念的某些方案理论问题，我们对某些脱节的还原群体的家庭进行了详细研究，我们称之为弱还原性的小组计划。我们的工作可用于为全球Galois表示形式生产几何升力，我们以$ \ mathrm {g} _2 $值表示表示为此进行了说明。
In this paper we study the universal lifting spaces of local Galois representations valued in arbitrary reductive group schemes when $\ell \neq p$. In particular, under certain technical conditions applicable to any root datum we construct a canonical smooth component in such spaces, generalizing the minimally ramified deformation condition previously studied for classical groups. Our methods involve extending the notion of isotypic decomposition for a $\textrm{GL}_n$-valued representation to general reductive group schemes. To deal with certain scheme-theoretic issues coming from this notion, we are led to a detailed study of certain families of disconnected reductive groups, which we call weakly reductive group schemes. Our work can be used to produce geometric lifts for global Galois representations, and we illustrate this for $\mathrm{G}_2$-valued representations.
