On sums of Betti numbers of affine varieties

We show that if V is a subvariety of the affine N-space defined by polynomials of degree at most d, then the sum of its $\mathrm{\ell }$-adic Betti numbers does not exceed $2(N+1{)}^{2N+1}(d+1{)}^N$. This answers a question of Katz (FFA 2001).