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Any characteristic zero field is an inductive limit of fields that can be embedded into complex numbers (i.e., those of characteristic 0 and of cardinality at most continuum). Hence the assumption t …

Let $f:X\to Y$ be a universal homeomorphism of schemes, $R$ a coefficient ring. Which assumptions on $f$ and $R$ are suffient to ensure that the pullback map $f^*$ of $R$-linear Chow groups is biject …

Is the Grothendieck's Standard Conjecture D (stating that the numerical equivalence relation for algebraic cycles with rational coefficients coincides with the homological one) known to be true for di …

In the paper Smirnov, Oleg N., Graded associative algebras and Grothendieck standard conjectures// Invent. Math. 128 (1997), no. 1, 201–206 it is proved that Standard Conjecture D (numerical equivalen …

This question is a continuation of Varieties with Chow groups supported in positive codimension: examples and properties? What examples are known of morphisms of varieties and Chow motives (say, over …

What can one say about the Chow group of zero-cycles (up to rational equivalence) for a product of smooth projective varieties and Chow motives (so, I am interested in the kernel $Chow_0(P)\otimes Cho …

In their 1983 paper "Remarks on correspondences and algebraic cycles" Bloch and Srinivas proved several interesting properties of smooth proper varieties (over universal domains) whose Chow groups of …

Are there any examples known of an affine variety $A$ over an algebraically closed field such some Chow group (say, of codimension at least $2$) of $A$ with coefficients in $\mathbb{Z}/n\mathbb{Z}$ ($ …

Let $P$ be a smooth projective variety. For an object $X$ of $D_{perf}(P)$ (i.e. a bounded perfect complex of $\mathfrak{O}_P$-module sheaves) we consider its class $[X]$ in $K_0(P)\otimes \mathbb{Q}( …

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 …

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 $ …

You may be interested in the following paper: Nilpotence theorem for cycles algebraically equivalent to zero, by Vladimir Voevodsky http://www.math.uiuc.edu/K-theory/0041/ (possibly, a newer version …