  We prove that wild ramification of a constructible sheaf on a surface is
determined by that of the restrictions to all curves. We deduce from this
result that the Euler-Poincar\'e characteristic of a constructible sheaf on a
variety of arbitrary dimension over an algebraically closed field is determined
by wild ramification of the restrictions to all curves. We similarly deduce
from it that so is the alternating sum of the Swan conductors of the cohomology
groups, for a constructible sheaf on a variety over a local field.
