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Search: MSC category 14C15 ( (Equivariant) Chow groups and rings; motives )

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1. CMB 2008 (vol 51 pp. 283)

Ravindra, G. V.
The Noether--Lefschetz Theorem Via Vanishing of Coherent Cohomology
We prove that for a generic hypersurface in $\mathbb P^{2n+1}$ of degree at least $2+2/n$, the $n$-th Picard number is one. The proof is algebraic in nature and follows from certain coherent cohomology vanishing.

Keywords:Noether--Lefschetz, algebraic cycles, Picard number
Categories:14C15, 14C25

2. CMB 2008 (vol 51 pp. 114)

Petrov, V.; Semenov, N.; Zainoulline, K.
Zero Cycles on a Twisted Cayley Plane
Let $k$ be a field of characteristic not $2,3$. Let $G$ be an exceptional simple algebraic group over $k$ of type $\F$, $^1{\E_6}$ or $\E_7$ with trivial Tits algebras. Let $X$ be a projective $G$-homogeneous variety. If $G$ is of type $\E_7$, we assume in addition that the respective parabolic subgroup is of type $P_7$. The main result of the paper says that the degree map on the group of zero cycles of $X$ is injective.

Categories:20G15, 14C15

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