论文标题
阿贝尔日志基本小组计划
Abelian Log Fundamental Group scheme
论文作者
论文摘要
让$ s $为连接的Dedekind方案，而$ x $是$ S $的合理平滑连接方案。令$ d $ d $分隔线不为$ x $，以使$ d $的不可约组件以及它们的交叉点在$ s $上平稳。现在，如果我们将$ x $与与$ d $相关的日志结构赋予结构，那么结构形态从$ x $到$ s $是log-s-Smooth。令$ x：s \ to x $为$ s $ point，以免与$ d $相交。然后，我们证明了$ x $的log nori基本组方案的最大阿贝里亚人适合$ 0 \ rightarrow的精确顺序（π^\ text {log} _ {\ text {nori}}（x，x））^{\ text {ab}} \ rightArrow \ text {n} {\ varprojlim} {\ varprojlim} \ varprojlim} \ mathbf {albf {alb} _ {alb} _ {x/s，x/s，d} _ {x/s，d} n n n 0. 0 n. 0 $ \ rowd。这里$ \ mathbf {ns}^τ_{x/s，d} $是通用的Neron-Severi组的扭转子组方案和$ \ Mathbf {alb} _ {alb} _ {x/s，d} $是与分区$ d $ $ d $相关的普遍化的Albanese方案。
Let $S$ be a connected Dedekind scheme and $X$ be a proper smooth connected scheme over $S$ . Let $D$ a divisor with no multiplicity of $X$ such that the irreducible components of $D$ and as well their intersections are smooth over $S$. Now if we endow $X$ with the log structure associated with $D$ then the structure morphism from $X$ to $S$ is log-smooth. Let $x: S \to X$ be a $S$-point such that it doesn't intersect $D$. Then we prove that the maximal abelian quotient of the log Nori fundamental group scheme of $X$ fits in to an exact sequence of the form $0 \rightarrow (\mathbf{NS}^τ_{X/S,D})^{\vee} \rightarrow (π^\text{log}_{\text{Nori}}(X,x))^{\text{ab}} \rightarrow \underset{n}{\varprojlim} \mathbf{Alb}_{X/S,D}[n] \rightarrow 0$. Here $\mathbf{NS}^τ_{X/S,D}$ is the torsion subgroup scheme of the generalized Neron-Severi group and $\mathbf{Alb}_{X/S,D}$ is the generalized Albanese scheme associated with the divisor $D$.
