Appears in collection : Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday

Characteristic cycle for l-adic sheaf was introduced by T. Saito after the existence of singular support by Beilinson. This measures the ramification of the sheaf, and can be viewed as a vast generalization of Swan conductor. Various compatibility with cohomological operation had been verified by Saito and Beilinson, but the compatibility of pushforward along proper morphism has been left open. In this talk, I wish to discuss this compatibility.