On Continuity of Local Epsilon Factors of ℓ-adic Sheaves

Abstract

Abstract Let $S$ be a noetherian scheme and $ Y\to S$ be a smooth morphism of relative dimension $1$. For a locally constant sheaf on the complement of a divisor in $Y$ flat over $S$, Deligne and Laumon proved that the universal local acyclicity is equivalent to the local constancy of Swan conductors. In this article, assuming the universal local acyclicity, we show an analogous result of continuity of local epsilon factors. We also give a generalization of this result to a family of isolated singularities.