B. Gordon

Absolute Chow-Künneth projectors for modular varieties

It is conjectured that Chow-Künneth projectors exist for any X . Note the cohomology classes of Pi are the Künneth components of the diagonal class in H ðX XÞ. So the conjecture is stronger than a conjecture of Grothendieck—Conjecture (C) in his standard conjectures, [Gr], [Kl]—that the Künneth components of the diagonal be classes of algebraic cycles. Further, the projectors Pi should satisfy additional properties, [Mu 2].

Letter from Jannsen to Gross on higher Abel-Jacobi maps

I can now answer your question1 concerning a “geometric” or “physical” description of the 2-extension class assigned to an algebraic cycle mapping to zero under the Abel-Jacobi map. I shall describe everything in the l-adic setting; similar results can be stated for every reasonable cohomology theory (as in 11.5 of [1] Jannsen, U.: Mixed motives and algebraic K-theory, Habilitationsschrift Regensburg 19882).

Griffiths Groups of Supersingular Abelian Varieties

The Griffiths group

The arithmetic and geometry of algebraic cycles

\Gr^r(X)

A Survey of the Hodge Conjecture for Abelian Varieties

of a smooth projective variety

Relative Chow-Künneth projectors for modular varieties

X

Topological and algebraic cycles in Kuga-Shimura varieties

over an algebraically closed field is defined to be the group of homologically trivial algebraic cycles of codimension

Chow motives of elliptic modular surfaces and threefolds

r

Algebraic cycles in families of abelian varieties over Hilbert-Blumenthal surfaces.

on

The approach to the Hodge conjecture via normal functions

X