  Leopoldt's Conjecture is a statement about the relationship between the
global and local units of a number field. Approximately the conjecture states
that the Z_p-rank of the diagonal embedding of the global units into the
product of all local units equals the Z-rank of the global units. The variation
we consider asks: Can we say anything about the Z_p-rank of the diagonal
embedding of the global units into the product of some local units? We use the
p-adic Schanuel Conjecture to answer the question in the affirmative and
moreover we give a value for the Z_p-rank (of the diagonal embedding of the
global units into the product of some local units) in terms of the Z-rank of
the global units and a property of the the local units included in the product.
