  Suppose L is any finite algebraic extension of either the ordinary rational
numbers or the p-adic rational numbers. Also let g_1,...,g_k be polynomials in
n variables, with coefficients in L, such that the total number of monomial
terms appearing in at least one g_i is exactly m. We prove that the maximum
number of isolated roots of G:=(g_1,...,g_k) in L^n is finite and depends
solely on (m,n,L), i.e., is independent of the degrees of the g_i. We thus
obtain an arithmetic analogue of Khovanski's Theorem on Fewnomials, extending
earlier work of Denef, Van den Dries, Lipshitz, and Lenstra.
