标题： 导出等价，阿勒巴诺斯簇，以及三维代数簇的zeta函数 显示英文标题

标题： Derived equivalence, Albanese varieties, and the zeta functions of 3-dimensional varieties

摘要： 我们证明了在任何代数闭域上，导出等价的光滑射影簇具有同源的阿贝尔簇，扩展了Popa和Schnell对$\mathbb{C}$上簇的证明。 我们将此结果应用于证明，在任何有限域上，维度为3或更小的导出等价的光滑射影簇具有相等的zeta函数。 显示英文摘要

摘要： We prove that derived equivalent smooth, projective varieties over any algebraically closed field have isogenous Albanese varieties, extending the proof of Popa and Schnell for varieties over $\mathbb{C}$. We apply this result to show that over any finite field, derived equivalent smooth, projective varieties of dimension 3 or less have equal zeta functions.