Higher bivariant Chow groups and motivic filtrations
نویسندگان
چکیده
منابع مشابه
Filtrations on Chow Groups and Transcendence Degree
For a smooth complex projective variety X defined over a number field, we have filtrations on the Chow groups depending on the choice of realizations. If the realization consists of mixed Hodge structure without any additional structure, we can show that the obtained filtration coincides with the filtration of Green and Griffiths, assuming the Hodge conjecture. In the case the realizations cont...
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Let X be a smooth projective variety over a field k and denote by CH(X) the group of codimension n cycles modulo rational equivalence on X. The structure of this group is largely unknown when n ≥ 2, especially when k is a “large” field such as the complex numbers. Beginning with the work of Bloch [Bl3] and Beauville [Be1,2], the Chow ring of an abelian variety was found to have some structure a...
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We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. The degree zero group agrees with the a...
متن کاملFiltrations on the Chow Groups and Transcendence Degree
For a smooth complex projective variety X defined over a number field, we have filtrations on the Chow groups depending of the choice of realizations. If the realization consists of mixed Hodge structure without any additional structure, we can show that the obtained filtration coincides with the filtration of Green and Griffiths, assuming the Hodge conjecture. In the case the realizations cont...
متن کاملHigher Chow Groups and Etale Cohomology
The main purpose of the present paper is to relate the higher Chow groups of varieties over an algebraically closed field introduced by S.Bloch [B1] to etale cohomology. We follow the approach suggested by the auther in 1987 during the Lumini conference on algebraic K-theory. The first and most important step in this direction was done in [SV1], where singular cohomology of any qfh-sheaf were c...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2011
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2011-05300-6