  We prove that the value of the critical probability for percolation on an
abelian Cayley graph is determined by its local structure. This is a partial
positive answer to a conjecture of Schramm: the function pc defined on the set
of Cayley graphs of abelian groups of rank at least 2 is continuous for the
Benjamini-Schramm topology. The proof involves group-theoretic tools and a new
block argument.
