论文标题
塞雷重量，galois变形环和本地模型
Serre weights, Galois deformation rings, and local models
论文作者
论文摘要
我们调查了有关什至关于算术群体的共同论的猜想的概括的最新进展，主要集中在“体重”方面。这与Breuil和Mézard的猜想（概括）与模块化表示理论的几何形状有关。最近，B。Levin，S。Morra和作者通过在混合特征中构建投射品种（本地模型）在驯服的通用环境中建立了这些猜想，其奇异性模型（在通用的情况下），这些模型具有腐烂的clois galois变形戒指，以使$ \ mathbb {q} Q {q prate small small small smill small smym smill smill small smill smill smill smill smill smill smill smym had hod theft fornibletional contration。
We survey some recent progress on generalizations of conjectures of Serre concerning the cohomology of arithmetic groups, focusing primarily on the "weight" aspect. This is intimately related to (generalizations of) a conjecture of Breuil and Mézard relating the geometry of potentially semistable deformation rings to modular representation theory. Recently, B. Levin, S. Morra, and the authors established these conjectures in tame generic contexts by constructing projective varieties (local models) 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.
