论文标题
减少了泰特·沙法雷维奇集团
Reduced Tate-Shafarevich group
论文作者
论文摘要
我们证明了一种通用椭圆形的calabi-yau的重建定理，就căldăraru而言，$ 3 $ folds。从我们的论点来看，当且仅当它们的通用纤维是派生的等值时，因此，两个通用的椭圆形的calabi-yau $ 3 $ folds在基础上是等于等效的线性。作为应用程序，我们对Knapp-Scheidegger-Schimannek提出的猜想给出了肯定的答案。也就是说，对于每一对椭圆形的calabi-yau $ 3 $ folds，我们证明它们共享相对的雅各布，并且是$ p^2 $ - 固定派生的等值。
We prove a sort of reconstruction theorem for generic elliptic Calabi-Yau $3$-folds in the sense of Căldăraru. From our argument it follows that two generic elliptic Calabi-Yau $3$-folds are derived-equivalent linear over the base if and only if their generic fibers are derived-equivalent. As an application, we give affirmative answers to the conjectures raised by Knapp-Scheidegger-Schimannek. Namely, for each pair of elliptic Calabi-Yau $3$-folds in their list we prove that they share the relative Jacobian and are $P^2$-linear derived-equivalent.
