Under cohomological assumptions on the real locus, vector bundle classification on smooth real affine surfaces and threefolds mirrors the algebraically closed case, including the first example of a non-stably-free projective module with trivial Chern classes over a 3-dimensional real affine algebra.
2511.15616 , primaryclass =
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Explicit polynomial representatives of the suspended Hopf map over Z are produced in motivic homotopy theory, from which an explicit rank-2 vector bundle on the Jouanolou device of P^3_Z is derived.
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On the cohomological classification of vector bundles on smooth real affine surfaces and threefolds
Under cohomological assumptions on the real locus, vector bundle classification on smooth real affine surfaces and threefolds mirrors the algebraically closed case, including the first example of a non-stably-free projective module with trivial Chern classes over a 3-dimensional real affine algebra.
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Exotic Hopf maps, weight shifting and applications to vector bundles
Explicit polynomial representatives of the suspended Hopf map over Z are produced in motivic homotopy theory, from which an explicit rank-2 vector bundle on the Jouanolou device of P^3_Z is derived.