On the continuous part of codimension two algebraic cycles on threefolds over a field
| dc.creator | Guletskii, Vladimir | |
| dc.date | 2006-10-10 | |
| dc.date | 2007-07-16 | |
| dc.date.accessioned | 2026-07-07T08:18:38Z | |
| dc.date.available | 2026-07-07T08:18:38Z | |
| dc.description | Let $X$ be a non-singular projective threefold over an algebraically closed field of any characteristic, and let $A^2(X)$ be the group of algebraically trivial codimension 2 algebraic cycles on $X$ modulo rational equivalence with coefficients in $\mathbb Q$. Assume $X$ is birationally equivalent to another threefold $X'$ admitting a fibration over an integral curve $C$ whose generic fiber $X'_{\bar η}$, where $\bar η=Spec(\bar {k(C)})$, satisfies the following three conditions: (i) the motive $M(X'_{\bar η})$ is finite-dimensional, (ii) $H^1_{et}(X_{\bar η},\mathbb Q_l)=0$ and (iii) $H^2_{et}(X_{\bar η},\mathbb Q_l(1))$ is spanned by divisors on $X_{\bar η}$. We prove that, provided these three assumptions, the group $A^2(X)$ is representable in the weak sense: there exists a curve $Y$ and a correspondence $z$ on $Y\times X$, such that $z$ induces an epimorphism $A^1(Y)\to A^2(X)$, where $A^1(Y)$ is isomorphic to $Pic^0(Y)$ tensored with $\mathbb Q$. In particular, the result holds for threefolds birational to three-dimensional Del Pezzo fibrations over a curve. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610341 | |
| dc.identifier | http://arxiv.org/abs/math/0610341 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134500 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C15; 14C25 | |
| dc.title | On the continuous part of codimension two algebraic cycles on threefolds over a field | |
| dc.type | text |