论文标题
通过log hard lefschetz的刚性品种的hodge对称性
Hodge symmetry for rigid varieties via log hard Lefschetz
论文作者
论文摘要
受到汉森和李的问题的激励，我们表明，在以下情况下，一个平稳且适当的刚性分析空间$ x $满足hodge对称性：（1）基本的非架构fieldean field $ k $是残留的特征零，（2）$ k $是$ p $ - $ p $ - $ p $ - $ x $ $ $ $ $ $ k $ k $ k. $ k $ k. $ k. $ k. $ k $ k. $ k. $ k $ k. $ k. $ k.减少。”'我们还以$ h^1 $的形式谴责了他们的结果版本，而无需使用可半固定滑轮的模量空间。所有这些都取决于Kato的Log Hard Lefschetz猜想的案例，我们以$ h^1 $和“组合类型”的日志方案证明了这一点。
Motivated by a question of Hansen and Li, we show that a smooth and proper rigid analytic space $X$ with projective reduction satisfies Hodge symmetry in the following situations: (1) the base non-archimedean field $K$ is of residue characteristic zero, (2) $K$ is $p$-adic and $X$ has good ordinary reduction, (3) $K$ is $p$-adic and $X$ has "combinatorial reduction."' We also reprove a version of their result, Hodge symmetry for $H^1$, without the use of moduli spaces of semistable sheaves. All of this relies on cases of Kato's log hard Lefschetz conjecture, which we prove for $H^1$ and for log schemes of "combinatorial type."
