Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Motivic obstruction to rationality of a very general cubic hypersurface
  in $\mathbb P^5$   Let $S$ be a smooth projective surface over a field. We introduce the notion
of integral decomposability and, respectively, the opposite notion of integral
indecomposability, of the transcendental motive $M^2_{\rm tr}(S)$. If the
transcendental motive is indecomposable rationally, then it is indecomposable
integrally. For example, $M^2_{\rm tr}(S)$ is rationally, and hence integrally
indecomposable if $S$ is an algebraic $K3$-surface whose motive is known to be
finite-dimensional. In the paper we prove that $M^2_{\rm tr}(S)$ is integrally
indecomposable when $S$ is the self-product of a smooth projective curve having
enough morphisms onto an elliptic curve with complex multiplication. This
applies, for example, when $S$ is the self-product of the Fermat sextic in
$\mathbb P^2$. Some refinement of the same technique yields that $M^2_{\rm
tr}(S_6)$ is integrally indecomposable, where $S_6$ is the Fermat sextic in
$\mathbb P^3$. This suggests a conjecture saying that the transcendental motive
of any smooth projective surface is integrally indecomposable. We prove in the
paper that if this motivic integral indecomposability conjecture is true, and
if the motive of any smooth projective surface is finite-dimensional, then a
very general cubic hypersurface in $\mathbb P^5$ is not rational.

23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org