Algebraic varieties with small Chow groups
نویسندگان
چکیده
منابع مشابه
Chow Groups, Chow Cohomology, and Linear Varieties
We compute the Chow groups and Fulton–MacPherson’s operational Chow cohomology ring for a class of singular rational varieties including toric varieties. The computation is closely related to the weight filtration on the ordinary cohomology of these varieties. We use the computation to answer one of the open problems about operational Chow cohomology: it does not have a natural map to ordinary ...
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These groups form an intriguing set of invariants. Despite the vast literature on this subject, the groups have been calculated only in very few cases, such as for the projective spaces. One of the goals of this note is to understand these invariants in case the variety has “few cycles” in the sense that rational and homological equivalence coincide for all m-cycles up to a certain rank m = s. ...
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Let X be a proper flat scheme over the ring of integers of a global field. We show that the Tate conjecture and the finiteness of the Chow group of vertical cycles on self-products of X implies the vanishing of the dual Selmer group of certain twists of tensor powers of representations occurring in the étale cohomology of X.
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Schoen gave the first examples of smooth complex projective varieties X and prime numbers l for which the Chow group of algebraic cycles modulo l is infinite [21]. In particular, he showed that this occurs for all prime numbers l with l ≡ 1 (mod 3), with X the product of three copies of the Fermat cubic curve x3 + y3 + z3 = 0. This is a fundamental example, showing how far motivic cohomology wi...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1998
ISSN: 2156-2261
DOI: 10.1215/kjm/1250518004