Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representability of Chow groups of codimension three cycles   In this note we are going to prove that if we have a fibration of smooth
projective varieties $X\to S$ over a surface $S$ such that $X$ is of dimension
four and that the geometric generic fiber has finite dimensional motive and the
first \'etale cohomology of the geometric generic fiber with respect to
$\mathbb {Q}_l$ coefficients is zero and the second \'etale cohomology is
spanned by divisors, then $A^3(X)$ (codimension three algebraically trivial
cycles modulo rational equivalence) is dominated by finitely many copies of
$A_0(S)$. Meaning that there exists finitely many correspondences $\Gamma_i$ on
$S\times X$, such that $\sum_i \Gamma_i$ is surjective from $\oplus A^2(S)$ to
$A^3(X)$.

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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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The categories of this paper are: supr-con