In this paper, we deal with the étale cohomology of a proper regular arithmetic scheme X with ${\mathbb{Z}}_p(r)$ and ${\mathbb{Q}}_p(r)$-coefficients, where the coefficients are complexes of étale sheaves that the author introduced in [SH]. We will prove that the étale cohomology of X with ${\mathbb{Q}}_p(r)$-coefficients agrees with the Selmer group of Bloch-Kato for any $r\geqq \mathrm{\text{dim}}(X)$. Using this fundamental result, we further discuss an approach to the study of zeta values (or residue) at $s=r$, via the étale cohomology with ${\mathbb{Z}}_p(r)$-coefficients, relating Tamagawa number conjecture of Bloch-Kato with a zeta value formula. As a consequence, we will obtain an unconditional example of an arithmetic surface for which the residue of its zeta function at $s=2$ is computed modulo rational numbers prime to p, for infinitely many p's.

在本文中，我们处理一个适当的规则运算方案的平展上同调X与${\mathbb{ž}}_p（\mathrm{[R}）$ 和 ${\mathbb{问}}_p（\mathrm{[R}）$-系数，其中系数是作者在[SH]中介绍的étale滑轮的复数。我们将证明X与${\mathbb{问}}_p（\mathrm{[R}）$系数与Bloch-Kato的Selmer小组达成共识， $\mathrm{[R}\geqq \mathrm{\text{暗淡}}（X）$。利用这一基本结果，我们进一步讨论了一种研究zeta值（或残基）的方法。$s=\mathrm{[R}$，通过étalecohomology与 ${\mathbb{ž}}_p（\mathrm{[R}）$系数，将Bloch-Kato的Tamagawa数猜想与zeta值公式相关联。结果，我们将获得一个无条件的算术曲面示例，其zeta函数的残基为$s=\mathrm{2个}$对无穷多个p的模有理数素数p进行模运算。