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Search: All articles in the CMB digital archive with keyword Chow group

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1. CMB 2016 (vol 59 pp. 824)

Karpenko, Nikita A.
Incompressibility of Products of Pseudo-homogeneous Varieties
We show that the conjectural criterion of $p$-incompressibility for products of projective homogeneous varieties in terms of the factors, previously known in a few special cases only, holds in general. Actually, the proof goes through for a wider class of varieties which includes the norm varieties associated to symbols in Galois cohomology of arbitrary degree.

Keywords:algebraic groups, projective homogeneous varieties, Chow groups and motives, canonical dimension and incompressibility
Categories:20G15, 14C25

2. CMB 2015 (vol 59 pp. 144)

Laterveer, Robert
A Brief Note Concerning Hard Lefschetz for Chow Groups
We formulate a conjectural hard Lefschetz property for Chow groups, and prove this in some special cases: roughly speaking, for varieties with finite-dimensional motive, and for varieties whose self-product has vanishing middle-dimensional Griffiths group. An appendix includes related statements that follow from results of Vial.

Keywords:algebraic cycles, Chow groups, finite-dimensional motives
Categories:14C15, 14C25, 14C30

3. CMB 2012 (vol 56 pp. 640)

Türkmen, İnan Utku
Regulator Indecomposable Cycles on a Product of Elliptic Curves
We provide a novel proof of the existence of regulator indecomposables in the cycle group $CH^2(X,1)$, where $X$ is a sufficiently general product of two elliptic curves. In particular, the nature of our proof provides an illustration of Beilinson rigidity.

Keywords:real regulator, regulator indecomposable, higher Chow group, indecomposable cycle

4. CMB 2002 (vol 45 pp. 213)

Gordon, B. Brent; Joshi, Kirti
Griffiths Groups of Supersingular Abelian Varieties
The Griffiths group $\Gr^r(X)$ of a smooth projective variety $X$ over an algebraically closed field is defined to be the group of homologically trivial algebraic cycles of codimension $r$ on $X$ modulo the subgroup of algebraically trivial algebraic cycles. The main result of this paper is that the Griffiths group $\Gr^2 (A_{\bar{k}})$ of a supersingular abelian variety $A_{\bar{k}}$ over the algebraic closure of a finite field of characteristic $p$ is at most a $p$-primary torsion group. As a corollary the same conclusion holds for supersingular Fermat threefolds. In contrast, using methods of C.~Schoen it is also shown that if the Tate conjecture is valid for all smooth projective surfaces and all finite extensions of the finite ground field $k$ of characteristic $p>2$, then the Griffiths group of any ordinary abelian threefold $A_{\bar{k}}$ over the algebraic closure of $k$ is non-trivial; in fact, for all but a finite number of primes $\ell\ne p$ it is the case that $\Gr^2 (A_{\bar{k}}) \otimes \Z_\ell \neq 0$.

Keywords:Griffiths group, Beauville conjecture, supersingular Abelian variety, Chow group
Categories:14J20, 14C25

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