## 172 Citations

Filtrations on Chow Groups and Transcendence Degree

- Mathematics
- 2002

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…

Hodge-theoretic invariants for algebraic cycles

- Mathematics
- 2003

In this paper we use Hodge theory to define a filtration on the Chow groups of a smooth, projective algebraic variety. Assuming the generalized Hodge conjecture and a conjecture of Bloch-Beilinson,…

Chow motives of elliptic modular surfaces and threefolds

- Mathematics
- 1996

The main result of this paper is the proof for elliptic modular threefolds of conjectures on the existence and structure of a filtration on the Chow groups of smooth projective varieties. In the form…

Chow-KDecomposition for Some Moduli Spaces 1

- Mathematics
- 2009

In this paper we investigate Murre's conjecture on the Chow-Kunneth decomposition for universal families of smooth curves over spaces which dominate the moduli space Mg, in genus at most 8 and show…

Algebraic cycles on a generalized Kummer variety

- Mathematics
- 2015

We compute explicitly the Chow motive of any generalized Kummer variety associated to any abelian surface. In fact, it lies in the rigid tensor subcategory of the category of Chow motives generated…

ON THE CHOW THEORY OF PROJECTIVIZATIONS

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2021

In this paper, we prove a decomposition result for the Chow groups of projectivizations of coherent sheaves of homological dimension
$\le 1$
. In this process, we establish the…

On the Chow Groups of Supersingular Varieties

- MathematicsCanadian Mathematical Bulletin
- 2002

Abstract We compute the rational Chow groups of supersingular abelian varieties and some other related varieties, such as supersingular Fermat varieties and supersingular $K3$ surfaces. These…

Motivic decomposition and intersection Chow groups, I

- Mathematics
- 1998

For a quasiprojective variety S, we define a category CHM(S) of pure Chow motives over S. Assuming conjectures of Grothendieck and Murre, we show that the decomposition theorem holds in CHM(S). As a…

Chow-Künneth decomposition for some moduli spaces.

- Mathematics
- 2009

In this paper we investigate Murre’s conjecture on the Chow–Kunneth decomposition for universal families of smooth curves over spaces which dominate the moduli space Mg, in genus at most 8 and show…

## References

SHOWING 1-10 OF 18 REFERENCES

Motivic sheaves and filtrations on Chow groups

- Mathematics
- 1994

Grothendieck's motives, as described in [Dem, K12, M a ] are designed as a tool to understand the cohomology of smooth projective varieties and the algebraic cycles modulo homological and numerical…

Motivic decomposition of abelian schemes and the Fourier transform.

- Mathematics
- 1991

such that the /-adic realization of h (A) is H (A, Qt). Recall that Chow motives are obtained from the category of smooth projective varieties over a field by a construction of Grothendieck using äs…

On the motive of an algebraic surface.

- Mathematics
- 1990

0.1. The theory of motives has been created by Grothendieck in order to understand better — among other things — the underlying "objects" of the cohomology groups and to explain their common…

Classical Motives

- Mathematics
- 1994

There is therefore little which is original contained in these pages. I have given a more or less complete proof of Murre’s result in §4, so as to make the comparison between the different…

Foundations of Algebraic Geometry

- Mathematics
- 1946

Algebraic preliminaries Algebraic theory of specializations Analytic theory of specializations The geometric language Intersection-multiplicities (special case) General intersection-theory The…

Mixed Motives and Algebraic K-Theory

- Mathematics
- 1990

Mixed motives for absolute hodge cycles.- Algebraic cycles, K-theory, and extension classes.- K-theory and ?-adic cohomology.

Letter to Murre, Febr

- 1991

Murre -Motivic decomposition of abelian schemes and the Fourier

- Journal reine und angew. Math
- 1991