发表机构
Institute for Advanced Study; Princeton University; Imperial College London; Harvard University（高等研究院; 普林斯顿大学; 伦敦帝国学院; 哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究\(\mathbb{Q}_p\)绝对伽罗瓦群晶体表示模p约化的惯性权重，通过棱柱技术使布雷伊尔 - 基辛模模p约化获\(\mu_p\)-等变结构，结合仿射格拉斯曼流形结果，明确塞尔权重猜想并证其消除方向。
AI 中文摘要
对于\(\mathbb{Q}_p\)的绝对伽罗瓦群的具有给定霍奇 - 泰特权重的晶体表示，我们得到了其模p约化的惯性权重的新约束。这使我们能够在\(\mathbb{Q}_p\)上非分歧连通约化群的L - 参数的一般性中明确地表述塞尔权重猜想，并证明该猜想的消除方向。证明使用棱柱技术表明，附着于晶体伽罗瓦表示的布雷伊尔 - 基辛模的模p约化获得了自然的\(\mu_p\)-等变结构。将此与仿射格拉斯曼流形的\(\mu_p\)-不动点的几何结果相结合，得出了我们的新约束。
英文摘要
For a crystalline representation of the absolute Galois group of Q_p, with given Hodge-Tate weights, we obtain new constraints on the inertial weights of its mod p reduction. This allows us to formulate an explicit Serre weight conjecture, in the generality of L-parameters for unramified connected reductive groups over Q_p, and to prove the elimination direction of this conjecture. The proof uses prismatic techniques to show that the reductions modulo p of the Breuil-Kisin modules attached to crystalline Galois representations acquire a natural μ_p-equivariant structure. Combining this with results on the geometry of the μ_p-fixed points of affine Grassmannians leads to our new constraint.
Comments88 pages. Section 2 updated to consider mu_N-fixed points for arbitrary N, with future applications in mind. Some simplifications in the proof of 5.5.1, and elaboration in Remark 5.5.9
