论文标题
étale驯服消失的周期$ [\ mathbb {a}^1_ {s}/\ mathbb {g} _ {m，s}] $
Étale tame vanishing cycles over $[\mathbb{A}^1_{S}/\mathbb{G}_{m,S}]$
论文作者
论文摘要
我们在$ [\ mathbb {a}^1_ {s}/\ mathbb {g} _ {m，s}] $上开发了一种驯服的消失周期的理论。我们展示了这种形式主义的一些理想特性，其中包括：与（strctly）Henselian特征上的驯服循环消失的兼容性，这与tame的理论消失了$ \ Mathbb {a}^1_ {1_ {s} $，与张力器产品的兼容性和二元性兼容。在上一节中，我们证明了由第二名作者介绍的单一不变性的消失周期是tame tame消失的循环$ [\ mathbb {\ mathb {a}^a}^1_ {s}^s}/s $ n的规范连续作用的同型固定点。
We develop a theory of tame vanishing cycles for schemes over $[\mathbb{A}^1_{S}/\mathbb{G}_{m,S}]$ in the context of étale sheaves. We show some desired properties of this formalism, among which: a compatibility with tame vanishing cycles over a (strctly) henselian trait, a compatibility with the theory of tame vanishing cycles over $\mathbb{A}^1_{S}$, a compatibility with tensor product and with duality. In the last section, we prove that monodromy-invariant vanishing cycles, introduced by the second named author, are the homotopy fixed points with respect to a canonical continuous action of $μ_{\infty}$ of tame vanishing cycles over $[\mathbb{A}^1_{S}/\mathbb{G}_{m,S}]$.
