As in title, what is the group cohomology set $H^1(\mathbb{Z},GL_n(\mathbb{Z}_p^{ur}))$ ?
Here the action of $\mathbb{Z}$ on $GL_n(\mathbb{Z}_p^{ur})$ is via Galois action: consider $\mathbb{Z}\rightarrow \widehat{\mathbb{Z}}\cong Gal(\mathbb{Q}_p^{ur}/\mathbb{Q}_p)$.
Does anyone computed this before or give me a hint?