43 citations · 140 across the 10 of their papers we have counts for
13 papers
A cellular absolute motivic ring spectrum representing Hermitian K-theory
K. Arun Kumar, Oliver Röndigs
In the Morel-Voevodsky motivic stable homotopy category of a quasi-compact quasi-separated scheme S, several candidates exist for a motivic spectrum representing hermitian K-theory…
The motivic Adams conjecture
Alexey Ananyevskiy, Elden Elmanto, Oliver Röndigs +1
We solve a motivic version of the Adams conjecture with the exponential characteristic of the base field inverted. In the way of the proof we obtain a motivic version of mod k Dold…
On very effective hermitian -theory
Alexey Ananyevskiy, Oliver Röndigs, Paul Arne Østvær
We argue that the very effective cover of hermitian -theory in the sense of motivic homotopy theory is a convenient algebro-geometric generalization of the connective real topol…
Vanishing in stable motivic homotopy sheaves
Kyle Ormsby, Oliver Röndigs, Paul Arne Østvær
We determine systematic regions in which the bigraded homotopy sheaves of the motivic sphere spectrum vanish.
The motivic Hopf map solves the homotopy limit problem for -theory
Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær
We solve affirmatively the homotopy limit problem for -theory over fields of finite virtual cohomological dimension. Our solution employs the motivic slice filtration and the fi…
The Grothendieck ring of varieties and algebraic K-theory of spaces
Oliver Röndigs
Waldhausen's algebraic K-theory machinery is applied to motivic homotopy theory, producing an interesting motivic homotopy type. Over a field F of characteristic zero, its path com…