论文标题
关于henselian常规戒指的典范高酒精学，价值为$ p $ - adicétaletate tate曲折
On étale hypercohomology of henselian regular local rings with values in $p$-adic étale Tate twists
论文作者
论文摘要
让$ r $是在混合特征$（0，p）$（0，p）$和$ k $的离散估值环上的一个可分配家庭的本地环的捕获量。在本文中，我们证明了étale高精度学组的同构$ \ operatorName {h}^{n+1} _ {\ mathrm {\ Mathrm {\ acute {e} t}}}}}}}}（r，r，\ mathfrak {t} \ operatorName {h}^{1} _ {\ Mathrm {\ Acute {e} $ p $ -adic Tate Twist和$ W_ {R}ω_ {\ log}^{n} $是对数Hodge-Witt Sheaf。作为一种应用，我们证明了GALOIS共同学组的局部全球原理，而不是曲线的功能场，而在出色的Henselian分离估价环上，混合特征的优质估值环。
Let $R$ be the henselization of a local ring of a semistable family over the spectrum of a discrete valuation ring of mixed characteristic $(0, p)$ and $k$ the residue field of $R$. In this paper, we prove an isomorphism of étale hypercohomology groups $\operatorname{H}^{n+1}_{\mathrm{\acute{e}t}}(R, \mathfrak{T}_{r}(n)) \simeq \operatorname{H}^{1}_{\mathrm{\acute{e}t}}(k, W_{r}Ω_{\log}^{n})$ for any integers $n\geq 0$ and $r>0$ where $\mathfrak{T}_{r}(n)$ is the $p$-adic Tate twist and $W_{r}Ω_{\log}^{n}$ is the logarithmic Hodge-Witt sheaf. As an application, we prove the local-global principle for Galois cohomology groups over function fields of curves over an excellent henselian discrete valuation ring of mixed characteristic.
