  In this paper, we give a purely geometric approach to the local
Jacquet-Langlands correspondence for GL(n) over a p-adic field, under the
assumption that the invariant of the division algebra is 1/n. We use the l-adic
etale cohomology of the Drinfeld tower to construct the correspondence at the
level of the Grothendieck groups with rational coefficients. Moreover, assuming
that n is prime, we prove that this correspondence preserves irreducible
representations. This gives a purely local proof of the local Jacquet-Langlands
correspondence in this case. We need neither a global automorphic technique nor
detailed classification of supercuspidal representations of GL(n).
