 Here Qℓ("i" ) denotes the "i"th Tate twist, which means that this representation of the Galois group "G" is tensored with the "i"th power of the cyclotomic character.The Tate conjecture states that the subspace "W""G" of "W" fixed by the Galois group "G" is spanned, as a Qℓ-vector space, by the classes of codimension-"i" subvarieties of "V".An algebraic cycle means a finite linear combination of subvarieties; so an equivalent statement is that every element of "W""G" is the class of an algebraic cycle on "V" with Qℓ coefficients.