24 citations · 58 across the 11 of their papers we have counts for
14 papers
The zeroth stable homotopy groups of motivic spheres over the integers
Oliver Röndigs
The main result determines the zeroth integral Milnor-Witt stem of the motivic sphere spectrum in the Morel-Voevodsky motivic stable homotopy category of the integers. The componen…
Slices of the special linear algebraic cobordism spectrum
Ahina Nandy, Oliver Röndigs, Egor Zolotarev
Let be a field of exponential characteristic . We compute the slices of , where is the special linear algebraic cobordism spectrum defin…
Hermitian -theory and Milnor-Witt motivic cohomology over
Håkon Kolderup, Oliver Röndigs, Paul Arne Østvær
The theme of this paper is to compute hermitian -groups in terms of the recently developed theory of Milnor-Witt motivic cohomology. Our approach makes use of the very effective…
The second stable homotopy groups of motivic spheres
Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær
We compute the 2-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of motivic cohomology and hermitian K-groups.
Endomorphisms of the projective plane and the image of the Suslin-Hurewicz map
Oliver Röndigs
The endomorphism ring of the projective plane over a field F of characteristic neither two nor three is slightly more complicated in the Morel-Voevodsky motivic stable homotopy cat…
Remarks on motivic Moore spectra
Oliver Röndigs
The term "motivic Moore spectrum" refers to a cone of an element in the motivic stable homotopy groups of spheres. This article discusses some properties of motivic Moore spectra,…
The homotopy groups of the η-periodic motivic sphere spectrum
Kyle Ormsby, Oliver Röndigs
We compute the homotopy groups of the η-periodic motivic sphere spectrum over a finite-dimensional field k with characteristic not 2 and in which -1 a sum of four squares. We also…
Hermitian -theory, Dedekind -functions, and quadratic forms over rings of integers in number fields
Jonas Irgens Kylling, Oliver Röndigs, Paul Arne Østvær
We employ the slice spectral sequence, the motivic Steenrod algebra, and Voevodsky's solutions of the Milnor and Bloch-Kato conjectures to calculate the hermitian -groups of rin…
Gigantic random simplicial complexes
Jens Grygierek, Martina Juhnke-Kubitzke, Matthias Reitzner +2
We provide a random simplicial complex by applying standard constructions to a Poisson point process in Euclidean space. It is gigantic in the sense that - up to homotopy equivalen…
Cellularity of hermitian K-theory and Witt theory
Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær
Hermitian K-theory and Witt-theory are cellular in the sense of stable motivic homotopy theory over any base scheme without points of characteristic two.
On the -inverted sphere
Oliver Röndigs
It is shown that the first and second homotopy groups of the -inverted sphere spectrum over a field of characteristic not two are zero. A cell presentation of higher Witt theory…
Motivic strict ring models for K-theory
Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær
It is shown that the K-theory of every noetherian base scheme of finite Krull dimension is represented by a strict ring object in the setting of motivic stable homotopy theory. The…
A universality theorem for Voevodsky's algebraic cobordism spectrum
I. Panin, K. Pimenov, O. Röndigs
An algebraic version of a theorem due to Quillen is proved. More precisely, for a ground field k we consider the motivic stable homotopy category SH(k) of P^1-spectra equipped with…
Calculus of functors and model categories
Georg Biedermann, Boris Chorny, Oliver Röndigs
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure. In this paper we construct various localizations of the pr…