Jens Hornbostel

Schubert calculus for algebraic cobordism

Abstract We establish a Schubert calculus for Bott–Samelson resolutions in the algebraic cobordism ring of a complete flag variety G/B extending the results of Bressler–Evens [Trans. Amer. Math. Soc. 331: 799–813, 1992] to the algebro-geometric setting.

Push-forwards for Witt groups of schemes

We define push-forwards for Witt groups of schemes along proper morphisms, using Grothendieck duality theory. This article is an application of results of the authors on tensor-triangulated closed categories to such structures on some derived categories of schemes together with classical derived functors.

Beta-elements and divided congruences

The f-invariant is an injective homomorphism from the 2-line of the Adams-Novikov spectral sequence to a group which is closely related to divided congruences of elliptic modular forms. We compute the f-invariant for two infinite families of β-elements and explain the relation of the arithmetic of divided congruences with the Kervaire invariant one problem.