论文标题
品种的拓扑重建定理
Topological reconstruction theorems for varieties
论文作者
论文摘要
我们在Zariski拓扑中研究torelli-type定理，以在任意领域中至少2种尺寸的尺寸。代替Hodge结构，我们在Weil除数上使用线性对等关系。使用此设置，我们证明了Bogomolov和Tschinkel的意义上的通用Torelli定理。这些证据在很大程度上依赖于Veblen和Young投射几何学的经典基本定理的新变体。 对于特征性0的无数代数闭合场上的适当正常品种，我们表明Zariski拓扑空间可用于恢复除数的线性对等关系。结果，我们表明，任何此类品种的基本方案都是由其Zariski拓扑空间唯一决定的。我们用它来证明Gabriel定理的拓扑版本，指出，在不可数的代数封闭特征0上，适当的正常品种由其可构造的Abelian obelian obelianétale滑轮类别确定。 我们还讨论了任意特征的猜想，将Zariski拓扑空间与适当的正常品种的完美相关。
We study Torelli-type theorems in the Zariski topology for varieties of dimension at least 2, over arbitrary fields. In place of the Hodge structure, we use the linear equivalence relation on Weil divisors. Using this setup, we prove a universal Torelli theorem in the sense of Bogomolov and Tschinkel. The proofs rely heavily on new variants of the classical Fundamental Theorem of Projective Geometry of Veblen and Young. For proper normal varieties over uncountable algebraically closed fields of characteristic 0, we show that the Zariski topological space can be used to recover the linear equivalence relation on divisors. As a consequence, we show that the underlying scheme of any such variety is uniquely determined by its Zariski topological space. We use this to prove a topological version of Gabriel's theorem, stating that a proper normal variety over an uncountable algebraically closed field of characteristic 0 is determined by its category of constructible abelian étale sheaves. We also discuss a conjecture in arbitrary characteristic, relating the Zariski topological space to the perfection of a proper normal variety.
