0
votes
1answer
153 views

Pull-back of algebraic cycles under holomorphic maps

Let $f:X \to Y$ be a holomorphic map between two smooth complex projective manifolds. Is there a good notion of pull-back of algebraic cycles by $f$ which preserves degree in the following sense: ...
4
votes
1answer
429 views

Questions on standard (motivic) conjectures

Over an (algebraically closed) characteristic $p$ field, is it known that the cohomological equivalence of cycles relation (with respect to $\mathbb{Q}_l$-adic \'etale cohomology) does not depend on ...
3
votes
1answer
276 views

Explain the relation between $K_0$ and morphisms of Chow motives

The Chern class yields an isomorphism $K_0(X)\otimes \mathbb Q\cong \bigoplus_{i\ge 0} Chow^i(X)\otimes \mathbb Q$ (for a smooth variety $X$ over a field?), whereas the latter group is isomorphic to ...
7
votes
0answers
365 views

Integral decomposition of the diagonal (Chow motives)

Let $k$ be a field of characteristic zero and let $X$ be a smooth proper varity over $k$ of dimension $d$. The K√ľnneth standard conjecture conjectures that there exist projectors $e_0, e_1, \ldots, ...
23
votes
4answers
2k views

difference between equivalence relations on algebraic cycles

For the definitions of the equivalence relations on algebraic cycles see http://en.wikipedia.org/wiki/Adequate_equivalence_relation. I want to know how far away from each other the equivalence ...
4
votes
1answer
386 views

Is the scalar extension functor for Chow motives conservative?

Denote $CHM(F)$ to be the category of Chow motives over a field $F$. Let's consider an algebraic exension $E/F$, then there is a natural extension of scalars functor $CHM(F) \to CHM(E)$. I was ...