论文标题
galois变形空间具有稀疏性自动点点
Galois deformation spaces with a sparsity of automorphic points
论文作者
论文摘要
令$ k/\ mathbb f_p $表示有限字段。对于任何分裂连接的还原组$ g/w（k）$和某些CM数字字段$ f $，我们将某些galois表示$ \overlineρ：gal（\ overline f/f）\ to g（k）$ to g（k）$ to连续家庭$ x _ {\ x _ {\ overlineρ} q_p}）$ upting $ \overlineρ$，使得$ x _ {\overlineρ} $的点的空间（在Fontaine-Mazur猜想的意义上）具有平行的Hodge-Tate权重，$ X _ {\ overlineCp} $。因此，$ x _ {\overlineρ} $中的一组点可以（猜想）与自动形式相关联。这概括了Calegari和Mazur的结果，以$ f/\ Mathbb Q $二次假想和$ G = GL_2 $。每cm $ f $ f $ f $ f $ f $ f $是一个完全真实的领域时，汽车的稀疏与$ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $的稀疏性相反，在这种情况下，汽车点通常被证明是密集的。
Let $k/\mathbb F_p$ denote a finite field. For any split connected reductive group $G/W(k)$ and certain CM number fields $F$, we deform certain Galois representations $\overlineρ:Gal(\overline F/F) \to G(k)$ to continuous families $X_{\overlineρ}$ of Galois representations $Gal(\overline F/F) \to G(\overline{\mathbb Q_p})$ lifting $\overlineρ$ such that the space of points of $X_{\overlineρ}$ which are geometric (in the sense of the Fontaine-Mazur conjecture) with parallel Hodge-Tate weights has positive codimension in $X_{\overlineρ}$. Thus the set of points in $X_{\overlineρ}$ which could (conjecturally) be associated to automorphic forms is sparse. This generalizes a result of Calegari and Mazur for $F/\mathbb Q$ quadratic imaginary and $G = GL_2$. The sparsity of automorphic points for $F$ a CM field contrasts with the situation when $F$ is a totally real field, where automorphic points are often provably dense.
