Let $n$ be either  $2$ or an odd integer greater than  $1$ , and fix a prime  $p>2(n+1)$ . Under standard ‘adequate image’ assumptions, we show that the set of components of $n$ -dimensional $p$ -adic potentially semistable local Galois deformation rings that are seen by potentially automorphic compatible systems of polarizable Galois representations over some CM field is independent of the particular global situation. We also (under the same assumption on  $n$ ) improve on the main potential automorphy result of Barnet-Lamb et al. [Potential automorphy and change of weight, Ann. of Math. (2) 179(2) (2014), 501–609], replacing ‘potentially diagonalizable’ by ‘potentially globally realizable’.

令$n$为 $2$或大于 $1$的奇数，并修正素数 $p>2(n+1)$。在标准的“适当图像”假设下，我们表明$n$ -维$p$ -adic 潜在半稳定局部 Galois 变形环的分量集是独立的特定的全球形势。我们还（在 $n$的相同假设下）改进了 Barnet-Lamb等人的主要潜在自同构结果。 [潜在的自构和体重变化，安。数学。(2) 179  (2) (2014), 501–609]，用“可能全局实现”代替“可能对角化”。