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

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1. CMB Online first

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 motivesCategories:14C15, 14C25, 14C30

2. 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 cycleCategory:14C25

3. 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 groupCategories:14J20, 14C25
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