Let $S$ be a strictly henselian trait of positive residue characteristic, let $X$ be a regular scheme semi-stable over $S$, let $D$ be a simple normal crossing divisor of $X$ containing the special fiber and let $F$ be a locally constant and constructibleétale sheaf on $U$ with certain ramification along $D$. In 2016, I. Leal conjectured a ramification bound for theétale cohomology of the sheaf $F$ on the geometric generic fiber. Abbes and Saito’s ramification theory is involved in her conjecture. In this talk, I will present a up-coming work proving her conjecture in a geometric setting, which extends a joint work with J.-B. Teyssier in 2018.