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On the integral Hodge conjecture for varieties with trivial Chow group
Humberto A. Diaz
We obtain examples of smooth projective varieties over that violate the integral Hodge conjecture and for which the total Chow group is of finite rank. Moreover, we sh…
A remark on the Rost Nilpotence Principle
Humberto A. Diaz
We consider a weak version of the Rost Nilpotence Principle. For characteristic zero fields k, we show that if it holds for all smooth projective schemes over k, then the Rost Nilp…
On the unramified cohomology of certain quotient varieties
Humberto A. Diaz
In this note, we consider unramified cohomology with coefficients for some (degree two) quotient varieties and describe a method that allows one to prove the non-van…
The Chow ring of a cubic hypersurface
Humberto A. Diaz
We study the product structure on the Chow ring (with rational coefficients) of a cubic hypersurface in projective space and prove that the image of the product map is as small as…
Rost nilpotence and higher unramified cohomology
Humberto A. Diaz
We develop an approach to proving the Rost nilpotence principle involving higher unramified cohomology. We use this to prove the principle for certain varieties of dimension $\leq…
Some nilpotence theorems for algebraic cycles
Humberto A. Diaz
Using fundamental results of Deligne, we prove a nilpotence theorem for algebraic cycles and use this to prove a torsion nilpotence result for correspondences on surfaces.
The Chow group mod for a product of elliptic curves
Humberto A. Diaz
Generalizing work of Schoen, we prove that the Chow group modulo of a product of or more very general complex elliptic curves is infinite.
The standard conjectures for the variety of lines on a cubic hypersurface
Humberto A. Diaz
The purpose of this note is to prove Grothendieck's standard conjectures for the Fano variety of lines on a smooth cubic hypersurface in projective space.
The motive of a smooth Theta divisor
Humberto A. Diaz
We prove a motivic version of the Lefschetz hyperplane theorem for a smooth ample divisor on an Abelian variety. We use this to construct a motive that realizes the primiti…
The motive of the Fano surface of lines
Humberto Diaz
The purpose of this note is to prove that the Chow motive of the Fano surface of lines on the smooth cubic threefold is finite-dimensional in the sense of Kimura. This gives an exa…