5 papers
Exotic Hopf maps, weight shifting and applications to vector bundles
Jean Fasel, William Hornslien
Using motivic homotopy theory we produce several explicit polynomial representatives of the suspension of the Hopf map defined over the integers. We derive from this computation an…
Splitting vector bundles over real algebraic varieties
Aravind Asok, Jean Fasel, Samuel Lerbet
Suppose is a smooth affine real variety and is a vector bundle over . We analyze the problem of splitting off a free rank one summand from in cor…
Algebraic vector bundles and -local A^1-homotopy theory
Aravind Asok, Jean Fasel, Michael J. Hopkins
Using techniques of A^1-homotopy theory, we produce motivic lifts of elements in classical homotopy groups of spheres; these lifts provide polynomial maps of spheres and allow us t…
On Tate Milnor-Witt Motives
Jean Fasel, Nanjun Yang
Smooth projective -varieties with isolated rational fixed points admit Tate Milnor-Witt motives. Over Euclidean fields, we give a splitting formula of such motives, w…
Suslin's cancellation conjecture in the smooth case
Jean Fasel
We prove that stably isomorphic vector bundles of rank d-1 on a smooth affine d-fold X over an algebraically closed field k are indeed isomorphic, provided d! is invertible in k. T…