论文标题
重量过滤的收敛络合物
Weight-filtered convergent complex
论文作者
论文摘要
使用日志收敛topoi，在％的派生类别中，％的衍生的类别，一个由％the Isostructure换出的，我们定义了两个基本过滤的复合物$（e_ {conv}，p）$和$（c_ {conv}，p），通过与一个相对简单的正常交叉交叉划分相对简单的crossing aviencor，$ p特征$ p特征$ p特征$ p> 0。使用$（c_ {cons}，p）$，我们证明了$ p $ - ad的纯度。作为推论，我们证明$（e_ {cons}，p）$和$（c_ {cons}，p）$是同构的。这些过滤的复合物产生了对数方案的对数收敛辅助分层的重量光谱序列。我们还将比较定理在$（e_ {cons}，p）$和$（c_ {cons}，p）$的投影之间与下面有限的下面限制的类别类别，该模块的Zariski topos的延过过滤的链链套件和log方案中的Zariski topos sheaves sheaves sheaves of log方案中的模块和iSozariskian过滤式的log complect $（e _} $}的限制范围{我们的上一本书。
Using log convergent topoi, %In the derived category of filtered complexes of %sheaves of modules over %an isostructure we define two fundamental filtered complexes $(E_{conv},P)$ and $(C_{conv},P)$ for the log scheme obtained by a smooth scheme with a relative simple normal crossing divisor over a scheme of characteristic $p>0$. Using $(C_{conv},P)$, we prove the $p$-adic purity. As a corollary of it, we prove that $(E_{conv},P)$ and $(C_{conv},P)$ are canonically isomorphic. These filtered complexes produce the weight spectral sequence of the log convergent cohomology sheaf of the log scheme. We also give the comparison theorem between the projections of $(E_{conv},P)$ and $(C_{conv},P)$ to the derived category of bounded below filtered complexes of sheaves of modules in the Zariski topos of the log scheme and the weight-filtered isozariskian filtered complex $(E_{zar},P)_{Q}$ of the log scheme defined in our previous book.
