论文标题
较高直接图像的几乎连贯性
Almost Coherence of Higher Direct Images
论文作者
论文摘要
对于具有几乎连贯的结构滑轮的方案之间有限表现的纯正确形态（在疲惫的意义上），我们证明了准共晶和几乎相干模块的较高直接图像是准共晶的，几乎是连贯的。我们的证明使用了Noetherian近似，灵感来自Kiehl的证据证明了更高直接图像的伪固定性。我们的结果使我们能够将Abbes-Gros的“ Faltings”的主要$ p $ -Adic比较定理在相对的情况下，用于针对方案的投影对数 - 平滑形态的相对案例，从而将相对的Hodge-Tate光谱序列构建。
For a flat proper morphism of finite presentation between schemes with almost coherent structural sheaves (in the sense of Faltings), we prove that the higher direct images of quasi-coherent and almost coherent modules are quasi-coherent and almost coherent. Our proof uses Noetherian approximation, inspired by Kiehl's proof of the pseudo-coherence of higher direct images. Our result allows us to extend Abbes-Gros' proof of Faltings' main $p$-adic comparison theorem in the relative case for projective log-smooth morphisms of schemes to proper ones, and thus also their construction of the relative Hodge-Tate spectral sequence.
