论文标题
Galois变形环和应用的本地模型
Local models for Galois deformation rings and applications
论文作者
论文摘要
我们在混合特征中构建了投射品种，其奇异性模型在一般情况下，具有较小的hodge-tate权重的$ \ mathbb {q} _p $的不受影响的扩展的诱人的结晶galois变形环。我们建立了有关它们的几何形状的几个重要事实，包括特殊点上的不底属性以及对其特殊纤维不可还原组成部分的理论描述。我们从这些几何结果中得出了许多本地和全球后果：Breuil-Mézard猜想在任意维度上的猜想，涉及较小的霍奇特（Hodge-tate）权重（具有适当的一般性条件）的潜在结晶变形环（具有适当的一般性条件），这是塞雷（Serre通用为$ p $），以及对塞雷（Serre）猜想的重量部分的无条件表述，以实现大受损表示。
We construct projective varieties in mixed characteristic whose singularities model, in generic cases, those of tamely potentially crystalline Galois deformation rings for unramified extensions of $\mathbb{Q}_p$ with small regular Hodge-Tate weights. We establish several significant facts about their geometry including a unibranch property at special points and a representation theoretic description of the irreducible components of their special fibers. We derive from these geometric results a number of local and global consequences: the Breuil-Mézard conjecture in arbitrary dimension for tamely potentially crystalline deformation rings with small Hodge-Tate weights (with appropriate genericity conditions), the weight part of Serre's conjecture for $U(n)$ as formulated by Herzig (for global Galois representations which satisfy the Taylor-Wiles hypotheses and are sufficiently generic at $p$), and an unconditional formulation of the weight part of Serre's conjecture for wildly ramified representations.
