Chow groups are finite dimensional, in some sense

By Shungen Kimura. 2005

262 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fee8f82f76eeb31f9501000afe1283c6c3db854f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

BLOCH'S CONJECTURE FOR CATANESE AND BARLOW SURFACES (2012, background): “Consider the codimension 2-cycle Γ ∈ CH2(S ×B S)Q. Assumption (1) tells us that the restricted cycle Γt := Γ|St×St is cohomologous to the sum of a cycle supported on a product of (nonnecessarily irreducible curves) in St and of cycles pulled-back from CH0(St) via the two projections.”
Chow motives versus non-commutative motives (2011, methodology): “Similarly to KMQ, the category CHMQ is obtained as the pseudo-abelianization of a category CHMQ whose objects are the smooth projective k-varieties.”
PROJECTORS ON THE INTERMEDIATE ALGEBRAIC JACOBIANS (2009, background): “They proved that for a surface S, CH0(S) is representable if and only if H 2(S,OS) = 0 and the Chow motive of S is finite dimensional.”
Motives and representability of algebraic cycles on threefolds over a field (2008, background): “By Kimura’s results, all abelian motives are finite-dimensional, see [13].”
Chow Rings, Decomposition of the Diagonal, and the Topology of Families (2014, methodology): “A completely different approach to such statements was initiated by Kimura [59], and it works concretely for those varieties that are dominated by products of curves.”
Algebraic cycles and fibrations (2012, background): “Let f : X → B be a generically smooth, projective and dominant morphism onto a smooth quasi-projective variety B defined over Ω.”
Surfaces of general type with geometric genus zero: a survey (2010, background): “1) The motive of a smooth projective curve is finite dimensional ([ Kim05 ], cor.”