9 citations · 19 across the 25 of their papers we have counts for
10 papers · 1 filter
Making the motivic group structure on the endomorphisms of the projective line explicit
Viktor Balch Barth, William Hornslien, Gereon Quick +1
We construct a group structure on the set of pointed naive homotopy classes of scheme morphisms from the Jouanolou device to the projective line. The group operation is defined via…
Representability of the local motivic Brouwer degree
Gereon Quick, Therese Strand, Glen Matthew Wilson
We study which quadratic forms are representable as the local degree of a map with an isolated zero at , following the work of Kass and Wickelgren who establis…
Examples of non-algebraic classes in the Brown-Peterson tower
Gereon Quick
For every , we construct classes in the Brown-Peterson cohomology of smooth projective complex algebraic varieties which are not in the image of the c…
Verdier hypercovering theorem for motivic spectra
Gereon Quick, Andreas Rosenschon
We prove a Verdier Hypercovering Theorem for cohomology theories arising from motivic spectra. This allows us to construct for smooth quasi-projective complex varieties a natural m…
An Abel-Jacobi invariant for cobordant cycles
Gereon Quick
We discuss an Abel-Jacobi invariant for algebraic cobordism cycles whose image in topological cobordism vanishes. The existence of this invariant follows by abstract arguments from…
Existence of rational points as a homotopy limit problem
Gereon Quick
We show that the existence of rational points on smooth varieties over a field can be detected using homotopy fixed points of etale topological types under the Galois action. As ou…