论文标题
派生的不变和动机，第二部分的积分派生不变和某些应用
Derived invariants and motives, Part II integral derived invariants and some applications
论文作者
论文摘要
在本文中，我们使用图案理论构建具有积分系数的新衍生不变式，并提供了多种应用。具体而言，我们获得以下结果：对于复杂的代数表面，我们证明Abelianized基本组中的某些扭转是一个不变的。我们证明，Hodge-Witt共同学组的集合是一个不变的。特别是，当特征足够大时，通过衍生的等效性保留了霍奇野事和普通还原。最后，使用非共同代数几何形状的技术，我们证明了Serre的普通密度猜想对于Cutic $ 4 $ -FOLDS是正确的，其中包含$ \ Mathbb {p}^2 $。
In this paper we construct new derived invariants with integral coefficients using the theory of motifs, and give several applications. Specifically, we obtain the following results: For complex algebraic surfaces, we prove that certain torsion in the abelianized fundamental group is a derived invariant. We prove that the collection of Hodge-Witt cohomology groups is a derived invariant. In particular, Hodge-Witt reduction and ordinary reduction are preserved by derived equivalence when the characteristic is sufficiently large. Finally, using the techniques of non-commutative algebraic geometry, we prove that Serre's ordinary density conjecture is true for cubic $4$-folds which contain a $\mathbb{P}^2$.
