We describe the completed local rings of the trianguline variety at certain points of integral weights in terms of completed local rings of algebraic varieties related to Grothendieck’s simultaneous resolution of singularities. We derive several local consequences at these points for the trianguline variety: local irreducibility, description of all local companion points in the crystalline case, combinatorial description of the completed local rings of the fiber over the weight map, etc. Combined with the patched Hecke eigenvariety (under the usual Taylor-Wiles assumptions), these results in turn have several global consequences: classicality of crystalline strictly dominant points on global Hecke eigenvarieties, existence of all expected companion constituents in the completed cohomology, existence of singularities on global Hecke eigenvarieties.

我们用与格洛腾迪克同时解决奇点相关的代数簇的完整局部环来描述在积分权的某些点上三角簇的完整局部环。我们在三角线簇的这些点上推导出几个局部结果：局部不可约性、晶体情况下所有局部伴点的描述、权重图上光纤完整局部环的组合描述等。与修补的 Hecke 特征簇相结合（在通常的泰勒-怀尔斯假设下），这些结果反过来又产生几个全局后果：全局 Hecke 特征变量上晶体严格主导点的经典性、完整上同调中所有预期伴生成分的存在、全局 Hecke 特征变量上奇点的存在。