Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth models of motivic spheres   We study the representability of motivic spheres by smooth varieties. We show
that certain explicit "split" quadric hypersurfaces have the $\mathbb
A^1$-homotopy type of motivic spheres over the integers and that the $\mathbb
A^1$-homotopy types of other motivic spheres do not contain smooth schemes as
representatives. We then study some applications of these
representability/non-representability results to the construction of new exotic
$\mathbb A^1$-contractible smooth schemes. Then, we study vector bundles on
even dimensional "split" quadric hypersurfaces by developing an
algebro-geometric variant of the classical construction of vector bundles on
spheres via clutching functions.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph