论文标题
分类轨迹和相对的Lefschetz-Verdier公式
Categorical traces and a relative Lefschetz-Verdier formula
论文作者
论文摘要
我们证明，在Noetherian基础方案上，用于局部无环对象的相对Lefschetz-Verdier定理。这是通过研究对称单体$ 2 $ 2 $ - 同类对应关系类别中的双重和痕迹来完成的。我们表明，局部环性等同于偶性，并推断出二元性保留局部环性。作为共同学对应类别类别的另一个应用，我们表明附近的周期函数在Henselian评估环上保留了双重，从而概括了Gabber定理。
We prove a relative Lefschetz-Verdier theorem for locally acyclic objects over a Noetherian base scheme. This is done by studying duals and traces in the symmetric monoidal $2$-category of cohomological correspondences. We show that local acyclicity is equivalent to dualizability and deduce that duality preserves local acyclicity. As another application of the category of cohomological correspondences, we show that the nearby cycle functor over a Henselian valuation ring preserves duals, generalizing a theorem of Gabber.
