  We will introduce a regularization for $p$-adic multiple zeta values and show
that the generalized double shuffle relations hold. This settles a question
raised by Deligne, given as a project in Arizona winter school 2002. Our
approach is to use the theory of Coleman functions on the moduli space of genus
zero curves with marked points and its compactification. The main ingredients
are the analytic continuation of Coleman functions to the normal bundle of
divisors at infinity and definition of a special tangential base point on the
moduli space.
