Around rationality of algebraic cycles

Deligne and Hain ([i] and [2]) each have defined functorial mixed Hodge struc- tures on 7Ti(X, Xo), X an algebraic variety. These vary as the point

Finally, we mention the following (probably not absolutely negligible) ad- vantage of the pesent presentation: it gives a uniform way to describe the weight filtration of

Chow group of codimension p cycles modulo rational equivalence on X and by Griffp(X) the subquotient of Ap(X) consisting of cycles which are homologically equivalent

These groups are a hybrid of algebraic geometry and algebraic topology: the 1-adic Lawson homology group LrH2,+i(X, Zi) of a projective variety X for a given prime

invariant theory, for the moduli space is the quotient variety PD /SL3 , where PD is the ((D+22)) - l)-dimensional projective space of homogeneous polynomials of

Let X be a smooth projective variety over an algebraically closed field k, and let CHO(X) be the Chow group of zero cycles on X modulo rational equivalence; further,

THEOREM 5.2: Let V be a threefold of general type, and suppose that for n sufficiently large, InKvl has no indeterminate locus and the.. fixed components are normal

Let X be a smooth projective algebraic variety defined over an algebraically closed field