Künneth projectors for open varieties

Murre's conjectures and explicit Chow--Kuenneth projectors for some varieties

In this paper, we investigate Murre's conjectures on the structure of rational Chow groups and exhibit explicit Chow--Kuenneth projectors for some examples. More precisely, the examples we study are the varieties which have a nef tangent bundle. For surfaces and threefolds which have a nef tangent bundle explicit Chow--Kuenneth projectors are obtained which satisfy Murre's conjectures and the motivic Hard Lefschetz theorem is verified.

Projectors on the intermediate algebraic Jacobians

Let $X$ be a complex smooth projective variety of dimension $d$. Under some assumption on the cohomology of $X$, we construct mutually orthogonal idempotents in $CH_d(X \times X) \otimes \Q$ whose action on algebraically trivial cycles coincides with the Abel-Jacobi map. Such a construction generalizes Murre's construction of the Albanese and Picard idempotents and makes it possible to give new examples of varieties admitting a self-dual Chow-Künneth decomposition satisfying the motivic Lefschetz conjecture as well as new examples of varieties having a Kimura finite dimensional Chow motive. Fo…

具有C^*-作用的射影簇的劳森同调

Lawson Homology for projective varieties with C^*-action

本文针对带C^*-作用的射影簇，建立了相容的整系数劳森同调分解，证明了相关提升的性质，推导了特定基维数下的比较映射性质，计算了对称多项式并给出多类应用。

A note on Grothendieck's standard conjectures of type C and D

Grothendieck conjectured in the sixties that the even Kunneth projector (with respect to a Weil cohomology theory) is algebraic and that the homological equivalence relation on algebraic cycles coincides with the numerical equivalence relation. In this note we extend these celebrated conjectures from smooth projective schemes to the broad setting of smooth proper dg categories. As an application, we prove that Grothendieck's original conjectures are invariant under homological projective duality. This leads to a proof of Grothendieck's conjectures in the case of intersections of quadrics, line…