论文标题
等源K3表面的邻居和算术
Neighbors and arithmetic of isogenous K3 surfaces
论文作者
论文摘要
我们使用晶格理论研究K3表面的同学类别。从各向同性brauer类开始，我们通过相邻晶格的旋塞方法构建同基因。我们还确定了等源K3表面的定义领域，并在数量字段上进行了研究。然后，我们将结果应用于有关K3表面的Brauer组和Néron-Severi晶格的有限性的猜想。
We use lattice theory to study the isogeny class of a K3 surface. Starting from isotropic Brauer classes, we construct isogenies via Kneser method of neighboring lattices. We also determine the fields of definition of isogenous K3 surfaces, and study Kneser construction over number fields. We then apply our results to relate conjectures about the finiteness of Brauer groups and Néron-Severi lattices of K3 surfaces.
