We are expected to solve a conjecture of the title. Precisely; **Conjecture A**: k:an algebraic number field v:a non archimedean place of k E:a motive with good reduction at v For E, we have a corresponding unramified l-adic representation. The image of the decomposition group of that representation is topologically generated by a Frobenius element. The conjecture is that the characteristic polynomial of that Frobenius is ℚ-coefficients and if E is pure of weight i, its roots in ℂ has absolute value Nv^i/2. Here Nv is the number of elements of the residue field of kv. We also have **Weil conjecture**; F:a finite field of q elements X:a smooth projective variety over F The characteristic polynomial of frobenius of its l-adic cohomology of degree i has absolute value q^i/2. In addition we have two **standard conjectures** on algebraic cycles; **Lefschetz standard conjecture** asserts that an abstract analogue of the Λ-operator of Hodge theory is induced by an algebraic cycle on two products of smooth projective varieties over an algebraic closed field. **Hodge standard conjecture** asserts that there is an abstract version of the Hodge index theorem for ℚ-vector space of classes of algebraic cycles. I have the following three questions. 1.Conjecture A and Weil conjecture both concern the roots of weight of a characteristic polynomial. How are these two related? 2.Weil conjecture is proved under the assumptions of Lefschetz and Hodge standard conjectures. Is the conjecture A also proved using them? 3.Is the conjecture A proved for abelian varieties over any number field? Thank you for your answers.