论文标题
$ \ mathbb {f} _ {\ ell} $的天鹅导体的变化
Variation of the Swan conductor of an $\mathbb{F}_{\ell}$-sheaf on a rigid disc
论文作者
论文摘要
本文介绍了$ \ Mathbb {f} _ {\ ell} $ - 在刚性单位光盘$ d $上的$ \ mathbb {f} _ {f} _ {f} _ {f} _ {f} _ {f} _ {f} _ {f} $ d $ d $ the Endect $ k $具有代数封闭式$ p pretarive $ p p p \ pe el n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n neq的天鹅的副导体的变化。我们将与$ \ Mathcal {f} $ a函数$ {\ rm sw} _ {\ rm as}（\ Mathcal {f}，\ cdot）：\ Mathbb {q} _ {Q} _ {\ geq 0} \ to \ to \ mathbb {q Mathb {q}在\ Mathbb {q} _ {\ geq 0} $中的每个$ t \处，沿归一化积分模型的特殊光纤限制了$ \ mathcal {f} $限制对半径$ t $的分子。我们证明此功能是连续的和分段线性的，有限的许多斜率都是整数。我们根据与$ \ Mathcal {f} $相关的特征周期，计算$ t \ in \ Mathbb {q} _ {Q} _ {\ geq 0} $，A（a）对数差分形式与RAMIFICY理论定义。
This article studies the variation of the Swan conductor of a lisse étale sheaf of $\mathbb{F}_{\ell}$-modules $\mathcal{F}$ on the rigid unit disc $D$ over a complete discrete valuation field $K$ with algebraically closed residue field of characteristic $p\neq \ell$. We associate to $\mathcal{F}$ a function ${\rm sw}_{\rm AS}(\mathcal{F}, \cdot): \mathbb{Q}_{\geq 0}\to \mathbb{Q}$, defined with the Abbes-Saito logarithmic ramification filtration, which measures, at each $t\in \mathbb{Q}_{\geq 0}$, the ramification of the restriction of $\mathcal{F}$ to the subdisc of radius $t$ along the special fiber of the normalized integral model. We prove that this function is continuous and piecewise linear, with finitely many slopes which are all integers. We compute the slope at $t\in \mathbb{Q}_{\geq 0}$ in terms of a characteristic cycle associated to $\mathcal{F}$, a (power of a) logarithmic differential form defined by ramification theory.
